Answer
$3-2\sqrt{6}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
