## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 38

#### Answer

$\dfrac{2\sqrt{a}-3}{2\sqrt{a}-\sqrt{b}}=\dfrac{4a+2\sqrt{ab}-6\sqrt{a}-3\sqrt{b}}{4a-b}$

#### Work Step by Step

$\dfrac{2\sqrt{a}-3}{2\sqrt{a}-\sqrt{b}}$ Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible: $\dfrac{2\sqrt{a}-3}{2\sqrt{a}-\sqrt{b}}=\dfrac{2\sqrt{a}-3}{2\sqrt{a}-\sqrt{b}}\cdot\dfrac{2\sqrt{a}+\sqrt{b}}{2\sqrt{a}+\sqrt{b}}=...$ $...=\dfrac{(2\sqrt{a}-3)(2\sqrt{a}+\sqrt{b})}{(2\sqrt{a})^{2}-(\sqrt{b})^{2}}=...$ $...=\dfrac{(2\sqrt{a})^{2}+2\sqrt{ab}-6\sqrt{a}-3\sqrt{b}}{4a-b}=\dfrac{4a+2\sqrt{ab}-6\sqrt{a}-3\sqrt{b}}{4a-b}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.