#### Answer

The simplified form of $\frac{3-9\sqrt 2}{6} $ is $\frac{1-3\sqrt 2}{2}$.

#### Work Step by Step

$\frac{3-9\sqrt 2}{6} $
Step 1: The highest common factor of 3 and 9 is 3. Hence, 3 and 9 can be divided by 3, and 3 can be taken outside the bracket:
$\frac{3(1-3\sqrt 2)}{6} $.
Step 2: 3 can be cancelled from both numerator and denominator and we will be left with
$\frac{1-3\sqrt 2}{2}$.