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: 61

Answer

$\text{The given complex fraction simplifies to }\dfrac{x + 1}{x - 1}$.

Work Step by Step

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