## Intermediate Algebra (6th Edition)

Published by Pearson

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

#### Answer

$-\dfrac{x}{x-1}$

#### 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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