Chapter 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-1 Rational Expressions and Equations

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Simplifying Rational Expressions 6.2 – Multiplication and Division of Rational Expressions 6.3 – Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator 6.4 – Addition and Subtraction of Rational Expressions 6.5 – Complex Fractions 6.6 – Solving Rational Equations 6.7 – Rational Equations: Applications & Problem Solving 6.8 – Variation Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-3 Simplifying Rational Expressions

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-4 Rational Expressions is an expression of the form, where p and q are polynomials and q  0. A rational expression is an expression of the form, where p and q are polynomials and q  0. Examples: Whenever a rational expression has a variable in the denominator, assume that the values that make the denominator 0 are excluded.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-5 Signs of a Fraction Three signs are associated with any fraction: the sign of the numerator, the sign of the denominator, and the sign of the fraction. Changing any two of the three signs of a fraction does not change the value of the fraction - a + b + sign of the numerator sign of the denominator sign of the fraction - a b a -b = a b - =

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-6 Simplifying A rational expression is simplified or reduced to lowest terms when the numerator and denominator have no common factors other than 1. Example: a)

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-7 Simplifying Rational Expressions 1.Factor both the numerator and denominator as completely as possible. 2.Divide out any factors common to both the numerator and denominator. Simplify

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-8 Factoring a Negative 1 Remember that when –1 is factored from a polynomial, the sign of each term in the polynomial changes. Example: – 3x + 10 = – 1(3x – 10) = –(3x – 10) Simplify