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 - Page 79: 62

Answer

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

Work Step by Step

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