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: 72

Answer

$\dfrac{y-1}{y+1}$

Work Step by Step

Simplify by multiplying the LCD (which is $y$) to both the numerator and the denominator to obtain: $=\dfrac{y(2-\frac{2}{y})}{y(2+\frac{2}{y})} \\=\dfrac{y(2)-y(\frac{2}{y})}{y(2)+y(\frac{2}{y})} \\=\dfrac{2y-2}{2y+2}$ Factor out $2$ in both the numerator and the denominator then cancel the common factor/s to obtain: $\require{cancel} =\dfrac{2(y-1)}{2(y+1)} \\=\dfrac{\cancel{2}(y-1)}{\cancel{2}(y+1)} \\=\dfrac{y-1}{y+1}$
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