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 - Page 53: 20


One way of showing that $\dfrac{1}{x} + \dfrac{1}{y}$ is not equal to $\dfrac{1}{x+y}$ is by letting $x=2$ and $y=2$. See the explanation below.

Work Step by Step

In general, $\dfrac{1}{x} +\dfrac{1}{y} \ne \dfrac{1}{x+y}$. To illustrate this, let $x=2$ and $y=2$ to have: $\dfrac{1}{2} + \dfrac{1}{2} \ne \dfrac{1}{2+2} \\\dfrac{2}{2} \ne \dfrac{1}{4} \\1 \ne \dfrac{1}{4}$
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