## Intermediate Algebra (12th Edition)

$3-2\sqrt{6}$
$\bf{\text{Solution Outline:}}$ To simplify the the given expression, $\dfrac{30-20\sqrt{6}}{10} ,$ find the $GCF$ of all the terms. Then, express all terms as factors using the $GCF.$ Finally, cancel the $GCF$ in all the terms. $\bf{\text{Solution Details:}}$ The $GCF$ of the coefficients of the terms, $\{ 30,-20,10 \},$ is $10$ since it is the highest number that can divide all the given coefficients. Writing the given expression as factors using the $GCF$ results to \begin{array}{l}\require{cancel} \dfrac{10\cdot3-10\cdot2\sqrt{6}}{10\cdot1} .\end{array} Cancelling the $GCF$ in every term results to \begin{array}{l}\require{cancel} \dfrac{\cancel{10}\cdot3-\cancel{10}\cdot2\sqrt{6}}{\cancel{10}\cdot1} \\\\= \dfrac{3-2\sqrt{6}}{1} \\\\= 3-2\sqrt{6} .\end{array}