Pre-CalculusSec 1.4 Rational Expressions

Objectives:•To review domain•To simplify rational expressions

Vocabulary

A quotient of two algebraic expressions is a fractional expression.

A rational expression is a fractional expression where both the numerator and denominator are polynomials.

Domain

The domain of an algebraic expression is the set of real numbers that the variable is permitted to have.

Some basic expressions and their domains.

x

1}0{: xD

x }0{: xD

x

1}0{: xD

Ex 1. Find the domain of each expression.

a)

b)

c)

132 2 xx

652 xx

x

5xx

:{ }D x all real numbers

}2,3{: xxD

}0{: xD

Class Work

Find the domain of each expression.

1. 2. xxx 934 63

52 2

t

t

Simplifying Rational Expressions

Ex 2. Simplify.a)

b)

2

12

2

xx

x

65

122

2

xx

xx

To multiply rational expressions, we use this property of fractions:

Multiplying Rational Expressions

A C AC

B D BD

Ex 3. Perform the indicated operation and simplfy.

1

123

168

322

2

x

x

xx

xx

Dividing Rational Expressions

To divide rational expressions, we use this property of fractions:

A C A D

B D B C

Ex 4. Perform the indicated operation and simplify.

65

43

4

42

2

2

xx

xx

x

x

Class WorkMultiply or divide and simplify.3) 4)

5)

5

4

16

252

2

x

x

x

x65

32

1892

942

2

2

2

yy

yy

yy

y

2811152

165

2

2

2

xxxx

xx

Adding & Subtracting Rational Expressions

To add or subtract rational expressions, we first find a common denominator and then use this property of fractions:

A B A B

C C C

Ex 4. Perform the indicated operation & simplfy.a)

b)

21

3

x

x

x

22 1

2

1

1

xx

Class Work

6)

7)

31

5

x

x

x

22 2

1

4

xx

x

Compound Fractions

A compound fraction is a fraction in which the numerator, the denominator, or both, are themselves fractional expressions.

Ex 5. Simplify

xy

yx

1

1

Common Errors to Avoid

Hw #4 p41 1,4,5,7,10,11,1522,25,27,34,39,42,45,49,51