Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.5 Rational Expressions - R.5 Exercises - Page 54: 60



Work Step by Step

The expressions are similar since they have the same denominator. Subtract the numerators together then copy the denominator to obtain: $=\dfrac{7x+8-(x+4)}{3x+2} \\=\dfrac{7x+8-x-4}{3x+2} \\=\dfrac{(7x-x)+(8-4)}{3x+2} \\=\dfrac{6x+4}{3x+2}$ Factor out $2$ in the numerator, then cancel the common factors to obtain: $\require{cancel} \\=\dfrac{2(3x+2)}{3x+2} \\=\dfrac{2\cancel{(3x+2)}}{\cancel{3x+2}} \\=\color{blue}{2}$
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