Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.5 Rational Expressions - R.5 Exercises: 18

Answer

$\color{blue}{(-\infty, 5) \cup (5, +\infty)}$

Work Step by Step

The denominator of a rational expression is not allowed to be equal to zero as it will make the expression undefined. Thus, $x-5\ne0 \\x \ne5$ This means that the value of $x$ can be any real number except $5$. Therefore, the domain of the given rational expression is the set of real numbers except $5$. In interval notation, the domain is: $\color{blue}{(-\infty, 5) \cup (5, +\infty)}$
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