Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.6 Rational Expressions - A.6 Assess Your Understanding - Page A53: 43


$\dfrac{4-x}{x-2}, \quad x\neq 2$

Work Step by Step

The denominators are additive inverses of each other so we factor out factoring $-1$ out of the denominator of the second rational as follows: \begin{align*} \frac{4}{x-2}+\frac{x}{2-x}&=\frac{4}{x-2}+\frac{x}{-(x-2)}\\ \\&=\frac{4}{x-2}+\frac{-x}{x-2}\\ \\&=\frac{4}{x-2}-\frac{x}{x-2}\\ \\&=\frac{4-x}{x-2}, \quad x\ne2 \end{align*}
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