Calculus with Applications (10th Edition)

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

Prerequisite Skills Diagnostic Test: 25

Answer

$$\frac{4+\sqrt{10}}{3}$$

Work Step by Step

To rationalize the denominator multiply by $\frac{4+\sqrt{10}} {4+\sqrt{10}}$ ($=1$) $$\frac{2}{4-\sqrt{10}}=\bigg(\frac{2}{4-\sqrt{10}}\bigg)\bigg(\frac{4+\sqrt{10}} {4+\sqrt{10}}\bigg)$$ $$=\frac{2(4+\sqrt{10})}{16-10}=\frac{2(4+\sqrt{10})}{6}=\frac{4+\sqrt{10}}{3}$$
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