Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.4 Polynomial and Rational Inequalities - 4.4 Assess Your Understanding - Page 219: 16

Answer

$(-\infty,-2)U(0,1)$

Work Step by Step

Step 1. Graph $R(x)=\frac{x}{(x-1)(x+2)}$ as shown in the figure. Step 2. The vertical asymptotes ($x=-2,1$) and a zero ($x=0$) divide the x-axis into four intervals $(-\infty,-2),(-2,0),(0,1),(1,\infty)$ Step 3. For $R(x)\lt0$, we can identify the solution intervals as $(-\infty,-2)U(0,1)$
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