Answer
$-1+\sqrt{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the the given expression, $
\dfrac{-5+5\sqrt{2}}{5}
,$ 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, $\{
-5,5,5
\},$ is $
3
$ 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{5\cdot(-1)+5\cdot1\sqrt{2}}{5\cdot1}
.\end{array}
Cancelling the $GCF$ in every term results to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{5}\cdot(-1)+\cancel{5}\cdot1\sqrt{2}}{\cancel{5}\cdot1}
\\\\=
\dfrac{-1+1\sqrt{2}}{1}
\\\\=
-1+\sqrt{2}
.\end{array}
