1. 8.5 Solving Rational Equations

2. Steps to solve Rational Equations
Find common denominator
Find restrictions
Cross out all denominators
Solve for x
Check for restricted values of x

3. Example 1 3 2
LCD:

4. 3 2
Example 2
LCD:

5. 3 8 16
Example 3
LCD:

6. Example 4
LCD:

7. 8-5 : Solving Rational Equations
Example 5
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8-5 : Solving Rational Equations

8. Therefore, the equation has no solution.
Example 6
(x – 2)
(x – 2) 5x
x – 2
3x + 4 =
5x = 3x + 4
2x = 4
No Solution
x = 2
The solution x = 2 is extraneous because it makes the denominators of the original equation equal to 0.
Therefore, the equation has no solution.
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8-5 : Solving Rational Equations

9. Example 7
LCD:

10. Example 8
LCD:

11. Example 9

12. Example 10

13. Example 11
LCD:

14. Example 12

15. Example 13