## Intermediate Algebra (6th Edition)

$\dfrac{x-25}{-3\sqrt[]{x}+15}$
Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $\dfrac{\sqrt[]{x}+5}{-3} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{x}+5}{-3}\cdot\dfrac{\sqrt[]{x}-5}{\sqrt[]{x}-5} \\\\= \dfrac{(\sqrt[]{x})^2-(5)^2}{-3\sqrt[]{x}+15} \\\\= \dfrac{x-25}{-3\sqrt[]{x}+15} .\end{array} Note that all variables are assumed to have positive real numbers.