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: 59



Work Step by Step

The expressions are similar since they have the same denominator. Subtract the numerators together then copy the denominator to obtain: $=\dfrac{17y+3-(-10y-18)}{9y+7} \\=\dfrac{17y+3-(-10y) -(-18)}{9y+7} \\=\dfrac{17y+3+10y+18}{9y+7} \\=\dfrac{(17y+10y)+(3+18)}{9y+7} \\=\dfrac{27y+21}{9y+7}$ Factor out $3$ in the numerator, then cancel the common factors to obtain: $\require{cancel} \\=\dfrac{3(9y+7)}{9y+7} \\=\dfrac{3\cancel{(9y+7)}}{\cancel{9y+7}} \\=\color{blue}{3}$
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