Section 7 4 Simplifying Complex Rational Expressions Copyright

Section 7. 4 Simplifying Complex Rational Expressions Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.

Simplifying Rational Expressions A complex rational expression (also called a complex fraction) has a fraction in either the numerator, or the denominator, or both. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 2

Complex Rational Expressions Procedure to Simplify a Complex Rational Expression: Adding and Subtracting 1. Add or subtract so that you have a single fraction in both the numerator and the denominator. 2. Divide the fraction in the numerator by the fraction in the denominator. This is done by inverting the fraction in the denominator and multiplying it by the numerator. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 3

Example Simplify. Add the fractions in the denominator. Divide. Simplify. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 4

Example Simplify. Add the fractions in the numerator and in the denominator. Divide. Simplify. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 5

Simplifying Rational Expressions Another way to simplify complex rational expressions is to multiply the numerator and the denominator by the LCD of all the denominators in the complex fraction. Procedure to Simplify a Complex Rational Expression: Multiplying by the LCD 1. Determine the LCD of all individual denominators occurring in the numerator and denominator of the complex rational expression. 2. Multiply both the numerator and the denominator of the complex rational expression by the LCD. 3. Simplify, if possible. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 6

Example Simplify by using the LCD. The LCD of all the denominators is c 2. Multiply each term by c 2. Simplify. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 7

Example Simplify by multiplying by the LCD. The LCD of all the denominators is 8 w. Multiply each term by 8 w. Simplify. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 8

Example Simplify by multiplying by the LCD. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 9