Answer
$\dfrac{q\sqrt{5+q}}{5+q}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}