Sheng-Fang Huang. 6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions.
6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2...
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6.4_Rational_Equations.notebook 1 November 14, 2016 Focus On ... Chapter 6 6.4 Rational Equations • identifying nonpermissible values in a rational equation • determining the solution to a rational equation algebraically • solving problems using a rational equation
Transcript of 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2...
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Focus On ...
Chapter 6 6.4 Rational Equations
• identifying nonpermissible values in a rational equation• determining the solution to a rational equation algebraically• solving problems using a rational equation
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To solve an equation that involves fractions, one method is of solving is to eliminate the denominator by multiplying through by the LCD (Lowest common denominator)
Example - Solve
We will use this to solve complicated rational equations
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6.4Example 1
Solve a Rational EquationSolve the following equation. What values are nonpermissible?
Continue Next Page
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1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply every term on both sides by the LCD to....
eliminate all of the denominators
5) Solve the resulting equation. (It may be linear or quadratic)
6) Compare solution to n.p.v, to make sure it isn't extraneous
The Steps
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2 Multiply each term on both sides of the equation by 6( z – 2)(z + 2).
1 1
1 1
1 1
1 1
1
1
1 Factor each denominator.
z ≠–2, 2
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Check:Substitute z = 5 into the original equation.
Right SideLeft Side
Left Side = Right Side
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6.4
Example 1: Your Turn
Answer y ≠ 3, 6; y = 12
Solve the equation. What are the nonpermissible values?
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
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6.4Example 2Solve a Rational Equation With an Extraneous RootSolve the equation. What are the nonpermissible values?
Continue Next Page
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
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1 Factor any factorable terms in the equation.
k ≠ –2, 22
1
11
1
1
1
11
Multiply each term by (k – 2)(k + 2)
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4 Check: Substitute k = 6 into the original equation.
Left Side Right Side
Left Side = Right Side
Therefore, the solution is k = 6.
3 –2 is a nonpermissible value and is called an extraneous solution.
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6.4
Example 2: Your Turn
Answer
Solve the equation. What are the nonpermissible values?
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
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