College Algebra (10th Edition)

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

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding: 61

Answer

$\displaystyle \frac{2x+h-2\sqrt{x^2+xh}}{h}$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{\sqrt{x+h}-\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}=\frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}-\sqrt{x})}{(\sqrt{x+h}+\sqrt{x})(\sqrt{x+h}-\sqrt{x})}=\frac{(\sqrt{x+h})^2-2\sqrt{x}\sqrt{x+h}+(\sqrt{x})^2}{(x+h)-x}=\frac{x+h+x-2\sqrt{x}\sqrt{x+h}}{h}=\frac{2x+h-2\sqrt{x}\sqrt{x+h}}{h}=\frac{2x+h-2\sqrt{x(x+h)}}{h}=\frac{2x+h-2\sqrt{x^2+xh}}{h}$
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