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: 37

Answer

$\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}=\dfrac{2a+\sqrt{ab}+2\sqrt{a}+\sqrt{b}}{4a-b}$

Work Step by Step

$\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}$ Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible: $\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}\cdot\dfrac{2\sqrt{a}+\sqrt{b}}{2\sqrt{a}+\sqrt{b}}=...$ $...=\dfrac{(\sqrt{a}+1)(2\sqrt{a}+\sqrt{b})}{(2\sqrt{a})^{2}-(\sqrt{b})^{2}}=\dfrac{2\sqrt{a^{2}}+\sqrt{ab}+2\sqrt{a}+\sqrt{b}}{4a-b}=...$ $...=\dfrac{2a+\sqrt{ab}+2\sqrt{a}+\sqrt{b}}{4a-b}$
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