College Algebra (10th Edition)

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: 56


$\displaystyle \frac{9-5\sqrt{3}}{3}$

Work Step by Step

We rationalize the denominator: $\displaystyle \frac{\sqrt{3}-1}{2\sqrt{3}+3}=\frac{(\sqrt{3}-1)((2\sqrt{3}-3))}{(2\sqrt{3}+3)(2\sqrt{3}-3)}=\frac{2\sqrt{3}\sqrt{3}-3\sqrt{3}-2\sqrt{3}+3}{(2\sqrt{3})^2-3^2}=\frac{2*3-5\sqrt{3}+3}{(4*3-9)}=\frac{9-5\sqrt{3}}{3}$
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