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: 41

Answer

$-\dfrac{1}{2-2\sqrt2}$

Work Step by Step

Rationalize the numerator by multiplying $1-\sqrt{2}$ to both the numerator and the denominator to have: $=\dfrac{1+\sqrt{2}}{2} \cdot \dfrac{1-\sqrt{2}}{1-\sqrt{2}} \\=\dfrac{1-2}{2-2\sqrt2} \\=-\dfrac{1}{2-2\sqrt2}$
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