College Algebra 7th Edition

Published by Brooks Cole

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 52: 77

Answer

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

Work Step by Step

After squaring, we find a common denominator for the fractions, add them, and simplify: $\displaystyle \sqrt{1+(\frac{x}{\sqrt{1-x^{2}}})^{2}}=\sqrt{1+\frac{x^{2}}{1-x^{2}}}=\sqrt{\frac{1-x^{2}}{1-x^{2}}+\frac{x^{2}}{1-x^{2}}}=\sqrt{\frac{1}{1-x^{2}}}=\frac{1}{\sqrt{1-x^{2}}}$

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