Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 660: 30

Answer

$(2-x)\sqrt[]{x-1}$

Work Step by Step

Simplifying each term and then combining like terms, the given expression, $\sqrt[]{4x-4}-\sqrt[]{x^3-x^2} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[]{4(x-1)}-\sqrt[]{x^2(x-1)} \\\\= \sqrt[]{(2)^2\cdot(x-1)}-\sqrt[]{(x)^2\cdot(x-1)} \\\\= 2\sqrt[]{x-1}-x\sqrt[]{x-1} \\\\= (2-x)\sqrt[]{x-1} .\end{array} * Note that it is assumed that all variables represent positive numbers.

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