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: 32

Answer

$-5 - \frac{5}{2}\sqrt{6}$

Work Step by Step

Rationalize the denominator by multiplying $2+\sqrt{6}$ to both the numerator and the denominator to have: $=\dfrac{5}{2-\sqrt{6}} \cdot \dfrac{2+\sqrt{6}}{2+\sqrt{6}} \\=\dfrac{10+5\sqrt{6}}{4-6} \\=\dfrac{10+5\sqrt{6}}{-2} \\=-5 - \frac{5}{2}\sqrt{6}$
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