Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - Guided Practice for Examples 2, 3 and 4 - Page 268: 13


$\displaystyle \frac{-6}{7-\sqrt{5}}=\frac{-42-6\sqrt{5}}{44}$

Work Step by Step

$\displaystyle \frac{-6}{7-\sqrt{5}}\qquad$ ...rationalize the denominator by multiplying it with its conjugate, $7+\sqrt{5}$. $=\displaystyle \frac{-6}{7-\sqrt{5}}\cdot\frac{7+\sqrt{5}}{7+\sqrt{5}}\qquad$ ...simplify. $=\displaystyle \frac{-42-6\sqrt{5}}{49+7\sqrt{5}-7\sqrt{5}-5}\qquad$ ...simplify the denominator. $=\displaystyle \frac{-42-6\sqrt{5}}{44}$
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