## Intermediate Algebra (12th Edition)

$\dfrac{q\sqrt{5+q}}{5+q}$
$\bf{\text{Solution Outline:}}$ To rationalize the denominator of the given expression, $\dfrac{q}{\sqrt{5+q}} ,$ 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{q}{\sqrt{5+q}}\cdot\dfrac{\sqrt{5+q}}{\sqrt{5+q}} \\\\= \dfrac{q\sqrt{5+q}}{(\sqrt{5+q})^2} \\\\= \dfrac{q\sqrt{5+q}}{5+q} .\end{array}