Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set: 40

Answer

$\dfrac{-7\sqrt[]{11}}{5x}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{\sqrt[]{99}}{5x}-\sqrt[]{\dfrac{44}{x^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{9\cdot11}}{5x}-\sqrt[]{\dfrac{4}{x^2}\cdot11} \\\\= \dfrac{\sqrt[]{(3)^2\cdot11}}{5x}-\sqrt[]{\left( \dfrac{2}{x}\right)^2\cdot11} \\\\= \dfrac{3\sqrt[]{11}}{5x}-\dfrac{2\sqrt[]{11}}{x} \\\\= \dfrac{3\sqrt[]{11}-5(2\sqrt[]{11})}{5x} \\\\= \dfrac{3\sqrt[]{11}-10\sqrt[]{11}}{5x} \\\\= \dfrac{-7\sqrt[]{11}}{5x} .\end{array} Note that variables are assumed to have positive values.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.