Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter R - Elementary Algebra Review - R.6 Rational Expressions and Equations - R.6 Exercise Set - Page 980: 16


The simplified form of the rational expression $\frac{x}{x+y}\div \frac{y}{x+y}$ is$\frac{x}{y}$.

Work Step by Step

$\frac{x}{x+y}\div \frac{y}{x+y}$ $\frac{A}{B}\div \frac{C}{D}=\frac{A}{B}\cdot \frac{D}{C}$ The reciprocal of $\frac{y}{x+y}$ is$\frac{x+y}{y}$ So, multiply the reciprocal of the divisor, $\begin{align} & \frac{x}{x+y}\div \frac{y}{x+y}=\frac{x}{x+y}\cdot \frac{x+y}{y} \\ & =\frac{\left( x \right)\left( x+y \right)}{\left( x+y \right)\left( y \right)} \end{align}$ Regroup and remove the factor equal to 1, $\begin{align} & \frac{x}{x+y}\div \frac{y}{x+y}=\frac{\left( x \right)\left( x+y \right)}{\left( x+y \right)\left( y \right)} \\ & =\frac{\left( x+y \right)\left( x \right)}{\left( x+y \right)\left( y \right)} \\ & =1\cdot \frac{\left( x \right)}{\left( y \right)} \\ & =\frac{x}{y} \end{align}$
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.