1. Fractional Equations and Extraneous Solutions
Solving Rational Equations (not graphing) (7.10)

2. POD Simplify this rational function. What is the shape of the graph?
What is the restriction for x?

3. Today we use rational expressions in equations– we solve for x.
Let’s start with this one.
The Method:
Determine restrictions for x– can’t divide by 0.
Find common denominator. Factoring can help.
Adjust all terms with common denominator.
Cancel the denominator in all terms.
Solve the equation– don’t forget the restrictions! Those are the extraneous solutions.

4. Follow the Method
Determine restrictions for x.

5. Follow the Method
x ≠ 2, -3
2. Find common denominator. Factoring can help.

6. Follow the Method
Adjust all terms with common denominator.

7. Follow the Method
Cancel the denominator in all terms.

8. Follow the Method
Solve the equation– don’t forget the restrictions! Those are the extraneous solutions.
In this case, x = 2 is extraneous.

9. Try another Use the same method to solve this equation.
What are the extraneous solutions?

10. Try another Use the same method to solve this equation.
How would you test these solutions?

11. Try another Use the same method to solve this equation.
What are the extraneous solutions?

12. Try another Use the same method to solve this equation.
Check the solutions.

13. Try another Use the same method to solve this equation.
What do you notice about the solutions?

14. Try another Use the same method to solve this equation.
This is true for every value of x. So, the solution set is all real numbers except 4 and -4.