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: 65

Answer

$\color{blue}{\dfrac{3x+y}{2x-y}}$

Work Step by Step

Factor out $-1$ in the denominator of the subtrahend to obtain: $=\dfrac{x+y}{2x-y} - \dfrac{2x}{-1(-y+2x)} \\=\dfrac{x+y}{2x-y} - \dfrac{-2x}{2x-y}$ The expressions are similar so subtract the numerators and copy the denominator to obtain: $=\dfrac{x+y-(-2x)}{2x-y} \\=\dfrac{x+y+2x}{2x-y} \\=\color{blue}{\dfrac{3x+y}{2x-y}}$
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