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 - 4.2 Properties of Rational Functions - 4.2 Assess Your Understanding - Page 197: 20


All real numbers except $-2$ and $\frac{1}{3}$.

Work Step by Step

Factor the denominator to obtain: $3x^2+5x-2=(3x-1)(x+2)$ The denominator cannot be $0$. Hence, $(3x-1)(x+2)\ne0\\ \longrightarrow 3x-1\ne0 \text{ and } x+2\ne0\\ \longrightarrow x\ne\frac{1}{3} \text{ and } x \ne -2$ Therefore, the domain is all real numbers except $-2$ and $\frac{1}{3}$.
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