Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 354: 37



Work Step by Step

Factoring the given expression, $ \dfrac{x+1}{1-x}+\dfrac{1}{x-1} ,$ results to \begin{array}{l}\require{cancel} \dfrac{x+1}{-(x-1)}+\dfrac{1}{x-1} \\\\= -\dfrac{x+1}{x-1}+\dfrac{1}{x-1} .\end{array} Combining the numerators and copying the similar denominator results to \begin{array}{l}\require{cancel} \dfrac{-(x+1)+1}{x-1} \\\\= \dfrac{-x-1+1}{x-1} \\\\= \dfrac{-x}{x-1} \\\\= -\dfrac{x}{x-1} .\end{array}
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