Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 67

Answer

$\dfrac{2-\sqrt{7}}{-5}=\dfrac{3}{5(2+\sqrt{7})}$

Work Step by Step

$\dfrac{2-\sqrt{7}}{-5}$ Multiply the numerator and the denominator of this expression by the conjugate of the numerator and simplify if possible: $\dfrac{2-\sqrt{7}}{-5}=\dfrac{2-\sqrt{7}}{-5}\cdot\dfrac{2+\sqrt{7}}{2+\sqrt{7}}=\dfrac{2^{2}-(\sqrt{7})^{2}}{-5(2+\sqrt{7})}=...$ $...=\dfrac{4-7}{-5(2+\sqrt{7})}=\dfrac{-3}{-5(2+\sqrt{7})}=\dfrac{3}{5(2+\sqrt{7})}$
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