Rational Equations

Section 8-6

Objectives

• Solve rational equations with one variable by CROSS MULTIPLYING

• Check answers for Extraneous Solutions

Extraneous Solutions

• Any solution that makes a denominator ZERO does not check. (Extraneous)

Solving Rational Equations

• Two basic methods

• 1. Cross Multiply two rational expressions to solve them

• 2. Set equation equal to ZERO and then get Common Denominator

Today• Cross Multiplying Method

Cross Multiplication Method

3

36

3

24

xx

)3(24)3(36 xx

722410836 xx

18012 x

15x

Example 2

3 2

9

x

x

( 3) 9(2)x x 2 3 18x x

2 3 18 0x x

( 6)( 3) 0x x

6

3

x

x

Example 3

06

42

x

x

x

x

6

42

x

x

x

x

)4()6)(2( xxxx

xxxx 4128 22

124 x

3x

EXAMPLE 1 Solve a rational equation by cross multiplying

Solve: 3x + 1 = 9

4x + 13

x + 1 = 94x + 1

Write original equation.

3(4x + 5) = 9(x + 1) Cross multiply.

12x + 15 = 9x + 9 Distributive property

3x + 15 = 9 Subtract 9x from each side.

3x = – 6 Subtract 15 from each side.

x = – 2 Divide each side by 3.

The solution is –2. Check this in the original equation.

ANSWER

Homework

• WS 12-5