1. Splash Screen

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

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

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

5. 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.
Example 1-1b

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

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

8. Factor the denominator.
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.
Zero Product Property or
Solve each equation.
Answer: B
Example 1-2b

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

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

11. Simplify
Answer: –x
Example 1-3b

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

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

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

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

16. Simplify
Answer:
Example 1-5b

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

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

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

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

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

22. Simplify
Answer:
Example 1-7c