1. 9.1 Multiplying and Dividing Rational Expressions Alg 2

2. Contents Lesson 9-1Multiplying and Dividing Rational Expressions Lesson 9-2Adding and Subtracting Rational Expressions Lesson 9-3Graphing Rational Functions Lesson 9-4Direct, Joint, and Inverse Variation Lesson 9-5Classes of Functions Lesson 9-6Solving Rational Equations and Inequalities

3. Lesson 1 Contents Example 1Simplify a Rational Expression Example 2Use the Process of Elimination Example 3Simplify by Factoring Out –1 Example 4Multiply Rational Expressions Example 5Divide Rational Expressions Example 6Polynomials in the Numerator and Denominator Example 7Simplify a Complex Fraction

4. Example 1-1a Simplify Look for common factors. 1 1 Factor. Simplify. Answer:

5. Example 1-1b Under what conditions is this expression undefined? A rational expression is undefined if the denominator equals zero. To find out when this expression is undefined, completely factor the denominator. Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3. These values are called excluded values.

6. Example 1-1c a.Simplify b.Under what conditions is this expression undefined? Answer: Answer: undefined for x = –5, x = 4, x = –4

7. Example 1-2a Multiple-Choice Test Item For what values of p isundefined? A 5 B –3, 5 C 3, –5 D 5, 1, –3 Read the Test Item You want to determine which values of p make the denominator equal to 0.

8. Example 1-2b Solve the Test Item Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator. Factor the denominator. Solve each equation. Answer:B Zero Product Property or

9. Example 1-2c Multiple-Choice Test Item For what values of p isundefined? A –5, –3, –2 B –5 C 5 D –5, –3 Answer:D

10. Example 1-3a Simplify Factor the numerator and the denominator. Simplify. Answer:or –a or 1 1 a 1

11. Example 1-3b Simplify Answer: –x

12. Example 1-4a Simplify Simplify. Answer:Simplify. Factor. 1111111 1111111

13. Example 1-4b Simplify Factor. 1111111 1111111 1 Answer:Simplify.

14. Example 1-4c Simplify each expression. a. b. Answer:

15. Example 1-5a Simplify Answer:Simplify. Factor. 1111111 1111111 Multiply by the reciprocal of divisor.

16. Example 1-5b Simplify Answer:

17. Example 1-6a Simplify Multiply by the reciprocal of the divisor. 1 –11 1 11 Answer:Simplify.

18. Example 1-6b Simplify Multiply by the reciprocal of the divisor. Simplify.Answer: Factor. 1 11 1

19. Example 1-6c Answer: 1 Simplify each expression. a. b. Answer:

20. Example 1-7a Simplify Express as a division expression. Multiply by the reciprocal of divisor.

21. Example 1-7b Factor. 11–1 1 11 Simplify.Answer:

22. Example 1-7c Simplify Answer:

23. End of Lesson 1