## Intermediate Algebra (12th Edition)

$\dfrac{3\sqrt{x+y}}{x+y}$
$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $\dfrac{3}{\sqrt{x+y}} ,$ multiply both the numerator and the denominator by the denominator. $\bf{\text{Solution Details:}}$ Multiplying both the numerator and the denominator by the denominator, the given expression is equivalent to \begin{array}{l}\require{cancel} \dfrac{3}{\sqrt{x+y}}\cdot\dfrac{\sqrt{x+y}}{\sqrt{x+y}} \\\\= \dfrac{3\sqrt{x+y}}{(\sqrt{x+y})^2} \\\\= \dfrac{3\sqrt{x+y}}{x+y} .\end{array}