College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 62

Answer

$\text{The given complex fraction simplifies to } \dfrac{y-2}{y+2}$.

Work Step by Step

$\displaystyle \begin{array}{ l l } =\dfrac{y\left( 2-\dfrac{2}{y}\right)}{y\left( 2+\dfrac{2}{y}\right)} & \begin{array}{{>{\displaystyle}l}} \mathrm{Multiply\ the\ numerator\ and\ denominator\ }\\ \mathrm{of\ the\ complex\ fraction\ by} \ y \text{(the LCD of all the fractions.)} \end{array}\\ & \\ =\dfrac{y-y\left(\dfrac{2}{y}\right)}{y+y\left(\dfrac{2}{y}\right)} & \mathrm{Apply\ the\ distributive\ property.}\\ & \\ =\dfrac{y-\dfrac{2y}{y}}{y+\dfrac{2y}{y}} & \mathrm{Multiply} \ y\ \mathrm{by} \ \dfrac{2}{y}.\\ & \\ =\dfrac{y-2\cdot \dfrac{y}{y}}{y+2\cdot \dfrac{y}{y}} & \mathrm{Apply\ the\ rule} \ \dfrac{ab}{c} =a\left(\dfrac{b}{c}\right).\\ & \\ =\dfrac{y-2}{y+2} & \mathrm{Apply\ the\ rule} \ \dfrac{a}{a} =1. \end{array}$
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