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: 15


$-(x+7), \quad x\ne2$

Work Step by Step

By factoring both denominator and numerator and canceling the common factors, we obtain: \begin{align*} \require{cancel} \dfrac{x^2+5x-14}{2-x}&=\dfrac{(x-2)(x+7)}{-(x-2)}\\ \\&=\dfrac{\cancel{(x-2)}(x+7)}{-\cancel{(x-2)}}\\ \\&=-(x+7), \quad x\ne2 \end{align*}
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