Answer
$\dfrac{1-3\sqrt{2}}{2}$
Work Step by Step
Factoring the $GCF=3$ and then cancelling the common factor between the numerator and the denominator, the given expression, $
\dfrac{3-9\sqrt{2}}{6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3(1-3\sqrt{2})}{6}
\\\\=
\dfrac{\cancel{3}(1-3\sqrt{2})}{\cancel{3}\cdot2}
\\\\=
\dfrac{1-3\sqrt{2}}{2}
.\end{array}