Answer
$5(\sqrt{2}+1)=5\sqrt{2}+5$
Work Step by Step
We rationalize the denominator:
$\displaystyle \frac{5}{\sqrt{2}-1}=\frac{5(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\frac{5(\sqrt{2}+1)}{2-1}=5(\sqrt{2}+1)=5\sqrt{2}+5$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 57
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