Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises: 95

Answer

$\color{blue}{\dfrac{x\sqrt[3]{2}-\sqrt[3]{5}}{x^3}}$

Work Step by Step

Simplify each radical term to obtain: $=\sqrt[3]{\dfrac{2}{(x^2)^3}}-\sqrt[3]{\dfrac{5}{(x^3)^3}} \\=\dfrac{\sqrt[3]{2}}{x^2}-\dfrac{\sqrt[3]{5}}{x^3}$ Make the terms similar using their LCD of $x^3$ to obtain: $=\dfrac{x\sqrt[3]{2}}{x^2(x)}-\dfrac{\sqrt[3]{5}}{x^3} \\=\dfrac{x\sqrt[3]{2}}{x^3} - \dfrac{\sqrt[3]{5}}{x^3}$ Subtract the numerators and retain the denominator to obtain: $=\color{blue}{\dfrac{x\sqrt[3]{2}-\sqrt[3]{5}}{x^3}}$
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