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: 97

Answer

$\frac{1}{x^2\sqrt{x^2-1}}$

Work Step by Step

First, re-write to make it in radical form: $\frac{\frac{x^2}{\sqrt{x^2-1}}-\sqrt{x^2-1}}{x^2}$ Then, make both denominators of the top fraction the same: $\frac{\frac{x^2}{\sqrt{x^2-1}}-\frac{\sqrt{x^2-1}\cdot\sqrt{x^2-1}}{\sqrt{x^2-1}}}{x^2}$ Because of the law of radicals $\sqrt[n] a \cdot \sqrt[n] b=\sqrt[n] {ab}$: $\frac{\frac{x^2}{\sqrt{x^2-1}}-\frac{\sqrt{(x^2-1)^2}}{\sqrt{x^2-1}}}{x^2}$ Simplify further: $\frac{\frac{x^2-(x^2-1)}{\sqrt{x^2-1}}}{x^2}=\frac{1}{\sqrt{x^2-1}}\cdot\frac{1}{x^2}=\frac{1}{x^2\sqrt{x^2-1}}$
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