College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises: 91

Answer

$\displaystyle\frac{x(\sqrt{x}-2)}{x-4}$

Work Step by Step

We multiply the numerator and denominator by $2-\sqrt{x}$ and use the fact that $(a-b)(a+b)=a^2-b^2$ to simplify: $\displaystyle \frac{x}{2+\sqrt{x}}=\frac{x}{2+\sqrt{x}}*\frac{2-\sqrt{x}}{2-\sqrt{x}}=\frac{2x-x\sqrt{x}}{2^{2}-(\sqrt{x})^{2}}=\frac{x(2-\sqrt{x})}{4-x}=\frac{x(\sqrt{x}-2)}{x-4}$
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.