## Intermediate Algebra (12th Edition)

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