1. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations

2. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 2 Rational Expressions and Equations 7.1Simplifying, Multiplying, and Dividing Rational Expressions 7.2Adding and Subtracting Rational Expressions 7.3Simplifying Complex Rational Expressions 7.4Solving Equations Containing Rational Expressions CHAPTER 7

3. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 3 Simplifying Complex Rational Expressions 1.Simplify complex rational expressions. 2.Simplify rational expressions with negative exponents. 7.3

4. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 4 Complex rational expression: A rational expression that contains rational expressions in the numerator and/or denominator. Examples:

5. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 5 Simplifying Complex Rational Expressions To simplify a complex rational expression, Method 1 1. If necessary, rewrite the numerator and/or denominator as a single rational expression 2. Rewrite as a horizontal division problem and simplify. Method 2 1. Multiply the numerator and denominator of the complex rational expression by the LCD of the fractions in the numerator and denominator. 2. Simplify.

6. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 6 Example —Method 1 Simplify. Solution The numerator and denominator of the complex fraction are already single fractions.

7. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 7 Example —Method 2 Simplify. Solution z

8. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 8 Example —Method 1 Simplify. Solution

9. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 9 continued y

10. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 10 Example —Method 2 Simplify. Solution

11. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 11 Example Simplify. Solution Multiply the numerator and denominator by the LCD of all the rational expressions. (Method 2)

12. Copyright © 2015, 2011, 2007 Pearson Education, Inc. 12 Example Simplify. Solution Rewrite using only positive exponents.