College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.1 - Functions - 3.1 Assess Your Understanding - Page 212: 90


$\displaystyle \frac{1}{\sqrt{x+h+1}+\sqrt{x+1}}$

Work Step by Step

... We will use the hint of the previous exercise, as f(x) has similar form $f(x)=\sqrt{x+1}$ $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}$ ... use the hint, rationalize with $\displaystyle \frac{\sqrt{x+h+1}+\sqrt{x+1}}{\sqrt{x+h+1}+\sqrt{x+1}}$ $=\displaystyle \frac{(x+h+1)-(x+1)}{h(\sqrt{x+h+1}+\sqrt{x+1})}$ $=\displaystyle \frac{h}{h(\sqrt{x+h+1}+\sqrt{x+1})}$ ... h cancels $=\displaystyle \frac{1}{\sqrt{x+h+1}+\sqrt{x+1}}$
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