Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.5 - Rational Expressions - Exercises - Page 49: 65


$\frac{1}{(\sqrt{x+2}+\sqrt x)}$

Work Step by Step

$\frac{\sqrt{x+2}-\sqrt x}{2}=\frac{(\sqrt{x+2}-\sqrt x)(\sqrt{x+2}+\sqrt x)}{2(\sqrt{x+2}+\sqrt x)}=\frac{x+2-x}{2(\sqrt{x+2}+\sqrt x)}=\frac{2}{2(\sqrt{x+2}+\sqrt x)}=\frac{1}{(\sqrt{x+2}+\sqrt x)}$
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