Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 42



Work Step by Step

$\frac{1}{x+1}+\frac{1}{x-1}$ Find the lowest common denominator (i.e. $(x+1)(x-1)$) and adjust the fractions accordingly: $=\frac{1\times (x-1)}{(x-1)(x+1)}+\frac{1\times (x+1)}{(x-1)(x+1)}$ Expand any brackets: $=\frac{x-1}{(x-1)(x+1)}+\frac{x+1}{(x-1)(x+1)}$ Combine the fractions: $=\frac{x-1+x+1}{(x-1)(x+1)}$ Collect the like terms: $=\frac{2x}{(x-1)(x+1)}$
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