1. 9-6 SOLVING RATIONAL EQUATIONS & INEQUALITIES Objectives: 1) The student will be able to solve rational equations. 2) The student will be able to solve rational inequalities.

2. Recall… How do we find the least common multiple for each of the following sets of values? 1) 6, 8 2) 1, 5, 11 3) 4x, 6, 3y

3. Rational Equations… Include any equation that contains one or more rational expressions. Example: Are easier to solve of the fractions are eliminated. This can be accomplished by multiplying each side of the equation by the least common denominator (LCD) Remember: when multiplying each side by the LCD, EACH TERM ON EACH SIDE must be multiplied. We are not allowed to have a denominator of ZERO!

4. Recall how to clear fractions to solve linear equations. Excluded Value(s):

5. Example 1 : Solve the rational equation. Then check your solution. Excluded Value(s):

6. Example 2 : Solve the rational equation. Then check your solution. Excluded Value(s):

7. Example 3: Solve the rational equation. Then check your solution. Excluded Value(s):

8. Example 4 : Solve the rational equation. Then check your solution. Excluded Value(s):

9. Example 5 : Solve the rational equation. Then check your solution. Excluded Value(s):

10. Rational Inequalities… Contain one or more rational expressions. Steps to Solve: 1) State the excluded values. 2) Solve the related equation. 3) Use these values to divide a number line into regions. Test a value in each region to determine which regions satisfy the original inequality. Remember: When you multiply or divide by a negative number, you must flip the inequality sign!

11. Example 5: Solve the rational inequality. Check and Graph your solution set. Excluded Value(s):

12. Example 6: Solve the rational inequality. Check and Graph your solution set. Excluded Value(s):

13. Example 7: Solve the rational inequality. Check and Graph your solution set. Excluded Value(s):