Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.7 - Polynomial and Rational Inequalities - Exercise Set - Page 413: 69

Answer

$(-\infty,-1)\cup(1,2)\cup(3,\infty)$

Work Step by Step

Step 1. Factor the inequality as $\frac{(x-2)(x+1)}{(x-3)(x-1)}\gt0$, Step 2. Identify the boundary points as $x=-1,1,2,3$ Step 3. Using the test points to examine the signs of the left side across the boundary points, we have $...(+)...(-1)...(-)...(1)...(+)...(2)...(-)...(3)...(+)...$ Thus the solutions are $(-\infty,-1)\cup(1,2)\cup(3,\infty)$ Step 4. We can express the solutions on a real number line as shown in the figure.
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