Precalculus (6th Edition) Blitzer

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

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 87: 106

Answer

The required solution is $\frac{a+b}{ab}$

Work Step by Step

We have the given expression $\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b}$. And the left-hand side of the given expression is $\frac{1}{a}+\frac{1}{b}$ Simplify the above expression: $\begin{align} & \frac{1}{a}+\frac{1}{b}=\frac{1}{a}\times \frac{b}{b}+\frac{1}{b}\times \frac{a}{a} \\ & =\frac{b}{ab}+\frac{a}{ba} \\ & =\frac{b+a}{ab} \\ & =\frac{a+b}{ab} \end{align}$ And the right-hand side of the given expression is $\frac{1}{a+b}$ So, $\frac{1}{a}+\frac{1}{b}\ne \frac{1}{a+b}$. Thus, the correct form of the given expression is $\frac{1}{a}+\frac{1}{b}=$ $\frac{a+b}{ab}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.