College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 78

Answer

$|x^{3}+\frac{1}{4x^{3}}|$

Work Step by Step

We distribute the squared term, simplify, factor, and simplify again. We take care to remember that $\sqrt{x^2}=|x|$ (not just $x$): $\sqrt{1+(x^{3}-\frac{1}{4x^{3}})^{2}}=\sqrt{1+x^{6}-\frac{2x^{3}}{4x^{3}}+\frac{1}{16x^{6}}}=\sqrt{1+x^{6}-\frac{1}{2}+\frac{1}{16x^{6}}}=\sqrt{x^{6}+\frac{1}{2}+\frac{1}{16x^{6}}} =\sqrt{(x^{3}+\frac{1}{4x^{3}})^{2}}=|x^{3}+\frac{1}{4x^{3}}|$
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