Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.7 Radicals - R.7 Exercises - Page R-29: 44


$\dfrac{2}{p+\sqrt{p(p-2)}} $

Work Step by Step

Rationalize the numerator by multiplying $\sqrt{p}+\sqrt{p-2}$ to both the numerator and the denominator to have: $=\dfrac{\sqrt{p}-\sqrt{p-2}}{\sqrt{p}} \cdot \dfrac{\sqrt{p}+\sqrt{p-2}}{\sqrt{p}+\sqrt{p-2}} \\=\dfrac{p-(p-2)}{p+\sqrt{p(p-2)}} \\=\dfrac{p-p-(-2)}{p+\sqrt{p(p-2)}} \\=\dfrac{0+2}{p+\sqrt{p(p-2)}} \\=\dfrac{2}{p+\sqrt{p(p-2)}} $
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