Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.4 Adding and Subtracting Rational Expressions - 7.4 Exercises - Page 589: 23



Work Step by Step

The rational expressions have the same denominator so they are similar. Subtract the numerators and copy the denominator to obtain: $=\dfrac{(m+7)-(4m+22)}{m+5}$ Subtract each term of the subtrahend to obtain: $=\dfrac{m+7-4m-22}{m+5} \\=\dfrac{-3m-15}{m+5}$ Factor out $-3$ in the numerator to obtain: $\\=\dfrac{-3(m+5)}{m+5}$ Cancel the common factors to obtain: $\\=\color{blue}{-3}$
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