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: 19


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

Work Step by Step

Factor the denominator to obtain: $2x^2-5x-3=(2x+1)(x-3)$ The denominator cannot be $0$ hence, $(2x+1)(x-3)\ne0\\ \longrightarrow 2x+1\ne0, \text{ and } x-3\ne0\\ \longrightarrow x\ne-\frac{1}{2}\text{ and } x\ne3$. Therefore the domain is all real numbers except $-\frac{1}{2}$ and $3$.
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