1. Rational Equations
Section 8-6

2. Objectives
Solve rational equations with one variable by CROSS MULTIPLYING
Check answers for Extraneous Solutions

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

4. 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

5. Today
Cross Multiplying Method

6. Cross Multiplication Method

7. Example 2

8. Example 3

9. Solve a rational equation by cross multiplying
EXAMPLE 1
Solve a rational equation by cross multiplying
Solve: 3
x + 1 = 9
4x + 1 3
x + 1 = 9
4x + 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

10. Homework
WS 12-5