Algebra and Trigonometry 10th Edition

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

Chapter 11 - 11.5 - The Binomial Theorem - 11.5 Exercises - Page 813: 65


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

Work Step by Step

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