Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set: 25

Answer

$4\sqrt{x-2}$

Work Step by Step

Factor the radicand of the first radical to obtain: $=\sqrt{9(x-2)}+\sqrt{x-2} \\=\sqrt{3^2(x-2)} + \sqrt{x-2} \\=3\sqrt{x-2} + \sqrt{x-2}$ RECALL: The distributive property states that for any real numbers a, b, and c: (1) $ac + bc = (a+b)c$ (2) $ac-bc=(a-b)c$ Use the rule (1) above to combine like terms and obtain: $=(3+1)\sqrt{x-2} \\=4\sqrt{x-2}$
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