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    Reciprocal Identities

    Pythagorean Identities

    Co-function Identities

    Addition Formulas

    sin (a + b) = sin a cos b + cos a sin b

    cos (a + b) = cos a cos b sin a sin b

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    Subtraction Formulas

    sin (a - b) = sin a cos b - cos a sin b

    cos (a - b) = cos a cos b + sin a sin b

    Double Angle Formulas

    sin 2a = 2 sin a cos a

    cos 2a = cos 2a sin 2a = 2 cos 2a 1 = 1 2 sin 2a

    Even-odd Identities

    Sum-to-product Formulas

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    Product-to-sum Formulas

    12.b.

    Take thecosine of to get

    Take thecotangent of to get 1.

    Take thecosecant of to get 2.

    Multiply by 1 to get

    http://mathway.com/glossary.aspx?=cosinehttp://mathway.com/glossary.aspx?=cosinehttp://mathway.com/glossary.aspx?=cotangenthttp://mathway.com/glossary.aspx?=cotangenthttp://mathway.com/glossary.aspx?=cosecanthttp://mathway.com/glossary.aspx?=cosecanthttp://mathway.com/glossary.aspx?=multiplyhttp://mathway.com/glossary.aspx?=cosinehttp://mathway.com/glossary.aspx?=cotangenthttp://mathway.com/glossary.aspx?=cosecanthttp://mathway.com/glossary.aspx?=multiply
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    Multiply by 2 to get 1.

    x=(1)

    Remove the parentheses around the expression1.

    x=1

    12.c.

    12.e.

    Squaring an expression is the same as multiplying the expression by itself2 times.

    Multiply each term in the first group by each term in the second group using the FOILmethod. FOIL stands for FirstOuterInnerLast, and is a method of multiplying two

    binomials. First, multiply the first two terms in each binomial group. Next,multiply the

    outer terms in each group, followed by the inner terms. Finally, multiply the last two

    terms in each group.

    Simplify the FOILexpression by multiplying and combining all like terms.

    Squaring an expression is the same as multiplying the expression by itself2 times.

    http://mathway.com/glossary.aspx?=multiplyhttp://mathway.com/glossary.aspx?=parentheseshttp://mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/detail.aspx?=342837http://mathway.com/glossary.aspx?=multiplyhttp://mathway.com/glossary.aspx?=parentheseshttp://mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expression
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    Multiply each term in the first group by each term in the second group using the FOIL

    method. FOIL stands for FirstOuterInnerLast, and is a method of multiplying two

    binomials. First, multiply the first two terms in each binomial group. Next,multiply the

    outer terms in each group, followed by the inner terms. Finally, multiply the last twoterms in each group.

    Simplify the FOILexpression by multiplying and combining all like terms.

    Remove the parentheses that are not needed from the expression.

    Since and are like terms, add to to get

    Since 4cos(x)sin(x) and -4cos(x)sin(x) are like terms, add -4cos(x)sin(x) to

    4cos(x)sin(x) to get 0.

    Since and are like terms, add to to get

    http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/detail.aspx?=646008http://www.mathway.com/detail.aspx?=646007http://www.mathway.com/detail.aspx?=287201http://www.mathway.com/detail.aspx?=538025http://www.mathway.com/detail.aspx?=538024http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=binomialhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=FOILhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=term
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    Replace with 5 using the identity

    5=y

    Since y is on the right-hand side of theequation, switch the sides so it is on the left-

    hand side of the equation.

    y=5

    12.f.

    Invert the trigonometric factorin the denominator.

    Invert the trigonometric factorin the denominator.

    Take thecosine of50 to get 0.64.

    Expand the exponent(2) to theexpression.

    Squaring a number is the same as multiplying the number by itself In

    this case, 0.64 squared is 0.41.

    http://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/detail.aspx?=709554http://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expression
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    Remove the parentheses around the expression0.41.

    Take thecosine of40 to get 0.77.

    Expand the exponent(2) to theexpression.

    Squaring a number is the same as multiplying the number by itself In

    this case, 0.77 squared is 0.59.

    0.41+(0.59)=y

    Remove the parentheses around the expression0.59.

    0.41+0.59=y

    Add 0.59 to 0.41 to get 1.

    1=y

    Since y is on the right-hand side of theequation, switch the sides so it is on the left-hand side of the equation.

    y=1

    http://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/detail.aspx?=545938http://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equation
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    12.g.

    Take thecosine of110 to get -0.34.

    Take thecosine of160 to get -0.94.

    Multiply-1 by the -0.94 inside the parentheses.

    Add 0.94 to -0.34 to get 0.6.

    Take thesine of70 to get 0.94.

    Take thecosine of20 to get 0.94.

    Add 0.94 to 0.94 to get 1.88.

    Expand the exponent(2) to theexpression.

    http://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=sinehttp://www.mathway.com/glossary.aspx?=sinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=sinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expression
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    Squaring a number is the same as multiplying the number by itself In this

    case, 0.6 squared is 0.36.

    Expand the exponent(2) to theexpression.

    Squaring a number is the same as multiplying the number by itself In

    this case, 1.88 squared is 3.53.

    (0.36)+(3.53)=y

    Remove the parentheses that are not needed from the expression.

    0.36+3.53=y

    Add 3.53 to 0.36 to get 3.89.

    3.89=y

    Since y is on the right-hand side of theequation, switch the sides so it is on the left-

    hand side of the equation.

    y=3.89

    12.h.

    http://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/detail.aspx?=904582http://www.mathway.com/detail.aspx?=904581http://www.mathway.com/detail.aspx?=545774http://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equation
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    Invert the trigonometric factorin the denominator.

    To add fractions, the denominators must be equal. Thedenominators can be made equal

    by finding the least common denominator(LCD). In this case, the LCD is

    Next, multiply each fraction by a factorof1 that will create the LCD in each of the

    fractions.

    Complete the multiplication to produce a denominatorof in each expression.

    Combine thenumerators of all expressions that have common denominators.

    Take thecosine of75 to get 0.259.

    Expand the exponent(2) to theexpression.

    http://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=multiplicationhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=multiplicationhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expression
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    Squaring a number is the same as multiplying the number by itself

    In this case, 0.259 squared is 0.067.

    Remove the parentheses around the expression0.067.

    Take thetangent of75 to get 3.732.

    Expand the exponent(2) to theexpression.

    Squaring a number is the same as multiplying the number by itself

    In this case, 3.732 squared is 13.928.

    Remove the parentheses around the expression13.928.

    Multiply0.067 by 13.928 to get 0.933.

    http://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=tangenthttp://www.mathway.com/glossary.aspx?=tangenthttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/detail.aspx?=372443http://www.mathway.com/detail.aspx?=536059http://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=tangenthttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiply
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    Multiply-1 by the 0.933 inside the parentheses.

    Subtract 0.933 from 1 to get 0.067.

    Take thecosine of75 to get 0.259.

    Expand the exponent(2) to theexpression.

    Squaring a number is the same as multiplying the number by itself

    In this case, 0.259 squared is 0.067.

    Divide0.067 by 0.067 to get 1.

    1=x

    http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=dividehttp://www.mathway.com/detail.aspx?=90060http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=cosinehttp://www.mathway.com/glossary.aspx?=exponenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=divide
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    Since x is on the right-hand side of theequation, switch the sides so it is on the left-

    hand side of the equation.

    x=1

    13.a.

    Replace with an equivalentexpression using the fundamental

    identities.

    Rewrite the expression using the identity.

    13.c.

    Multiply by each term inside the parentheses.

    Remove the parentheses around the expression

    http://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/detail.aspx?=130498http://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expression
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    Replace with an equivalentexpression using the fundamental identities.

    Replace with an equivalentexpression using the fundamental

    identities.

    Remove the common factors that were cancelled out.

    Combine all similarvariables in the expression.

    To add fractions, the denominators must be equal. The denominators can be made

    equal by finding the least common denominator(LCD). In this case, the LCD is

    Next, multiply each fraction by a factorof1 that will create the LCD in

    each of the fractions.

    Complete the multiplication to produce a denominatorof in each

    expression.

    http://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=similarhttp://www.mathway.com/glossary.aspx?=variablehttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=multiplicationhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=similarhttp://www.mathway.com/glossary.aspx?=variablehttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=LCDhttp://www.mathway.com/glossary.aspx?=fractionhttp://www.mathway.com/glossary.aspx?=multiplicationhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expression
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    Combine the numerators of all expressions that have common denominators.

    Replace with 1 using the identity

    Replace with an equivalentexpression in the numerator.

    Since x is on the right-hand side of the equation, switch the sides so it is on the

    left-hand side of the equation.

    13.e.

    Since 1 does not contain the variable to solve for, move it to the right-hand side

    of the equation by subtracting 1 from both sides.

    Simplify the right-hand side of the equation.

    http://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=variablehttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/detail.aspx?=994940http://www.mathway.com/detail.aspx?=636134http://www.mathway.com/detail.aspx?=43303http://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=variablehttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equation
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    Multiply each term in the equation by -1.

    Multiply-x by -1 to get x.

    Simplify the right-hand side of the equation by simplifying each term.

    Replace with using the identity

    Factorout the GCF of from each term in the polynomial.

    Factorout the GCF of from

    Reduce the expression by canceling out the common factorof from

    http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=GCFhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=polynomialhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=GCFhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/detail.aspx?=190130http://www.mathway.com/detail.aspx?=353748http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=GCFhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=polynomialhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=GCFhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factor
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    the numeratorand denominator.

    Reduce the expression by canceling out the common factorof from

    the numeratorand denominator.

    13.f.

    Replace with using the identity

    Replace with using the identity

    Remove the extra parentheses around the factors.

    Multiply by each term inside the parentheses.

    http://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/detail.aspx?=180644http://www.mathway.com/detail.aspx?=180644http://www.mathway.com/detail.aspx?=548937http://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheses
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    Rewrite the factorof using the identity which in this case leads to

    Reduce the expression by canceling out the common factors.

    1=x

    Since x is on the right-hand side of theequation, switch the sides so it is on the left-

    hand side of the equation.

    x=1

    13.g.

    Since x is on the right-hand side of the equation, switch the sides so it is on the

    left-hand side of the equation.

    Multiply each term by a factorof1 that will equate all the denominators. In this

    case, all terms need a denominatorof The

    expression needs to be multiplied by to make the denominator

    The expression needs to be multiplied by

    to make the denominator

    http://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=identityhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominator
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    Multiply the expression by a factorof1 to create the least common denominator

    (LCD) of

    Remove the parentheses around the expression

    Multiply the expression by a factorof1 to create the least common denominator

    (LCD) of

    Remove the parentheses around the expression

    The numerators ofexpressions that have equal denominators can be combined. In

    this case, and have the same

    denominatorof so the numerators can be combined.

    Simplify the numeratorof the expression.

    http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/detail.aspx?=293006http://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=factorhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=denominatorhttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=combinehttp://www.mathway.com/glossary.aspx?=numeratorhttp://www.mathway.com/glossary.aspx?=expression
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    Since and are like terms, subtract from to get 0.

    13.h.

    Convert the to its equivalent.

    Multiply by each term inside the parentheses.

    Remove the parentheses around the expression

    Since x is on the right-hand side of the equation, switch the sides so it is on the

    left-hand side of the equation.

    http://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/detail.aspx?=792886http://www.mathway.com/detail.aspx?=792884http://www.mathway.com/detail.aspx?=293007http://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=equivalenthttp://www.mathway.com/glossary.aspx?=multiplyhttp://www.mathway.com/glossary.aspx?=termhttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=parentheseshttp://www.mathway.com/glossary.aspx?=expressionhttp://www.mathway.com/glossary.aspx?=equationhttp://www.mathway.com/glossary.aspx?=equation
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    14.a