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 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 88


$\displaystyle \frac{x+3\sqrt{x}-10}{x-25}$

Work Step by Step

We lose the square roots in the denominator by applying the difference of squares formula: $(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$ $\displaystyle \frac{\sqrt{x}-2}{\sqrt{x}-5}\color{red}{ \cdot\frac{\sqrt{x}+5}{\sqrt{x}+5} }\qquad$ (rationalize) $=\displaystyle \frac{(\sqrt{x}-2)(\sqrt{x}+5)}{(\sqrt{x})^{2}-(5)^{2}}$ ... use FOIL for the numerator $=\displaystyle \frac{(\sqrt{x})^{2}+5\sqrt{x}-2\sqrt{x}-10}{x-25}$ $=\displaystyle \frac{x+3\sqrt{x}-10}{x-25}$
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.