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

## Presentation on theme: "Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations."— Presentation transcript:

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

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

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

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:

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.

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.

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

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

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

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)

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