Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 44: 77



Work Step by Step

$\sqrt{1+\Big(\dfrac{x}{\sqrt{1-x^{2}}}\Big)^{2}}$ Evaluate the power inside the root: $\sqrt{1+\Big(\dfrac{x}{\sqrt{1-x^{2}}}\Big)^{2}}=\sqrt{1+\dfrac{x^{2}}{1-x^{2}}}=...$ Evaluate the sum of fractions inside the root: $...=\sqrt{\dfrac{1-x^{2}+x^{2}}{1-x^{2}}}=\sqrt{\dfrac{1}{1-x^{2}}}$
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