College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 72: 75


$\displaystyle \frac{x+1}{x-1}$

Work Step by Step

$\displaystyle \frac{1+\frac{1}{x}}{1-\frac{1}{x}}=(1+\frac{1}{x})\div(1-\frac{1}{x})$ $=(\displaystyle \frac{x}{x}+\frac{1}{x})\div(\frac{x}{x}-\frac{1}{x})$ $=\displaystyle \frac{x+1}{x}\div\frac{x-1}{x}$ ... division = multiplication with the reciprocal, $=\displaystyle \frac{x+1}{x}\cdot\frac{x}{x-1}$ ... x cancels, $=\displaystyle \frac{x+1}{x-1}$
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