Algebra

$\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}$

is equal to

$-\frac{17}{6} + \frac{1}{3\sqrt2} - 3\sqrt2 - \frac{1}{3\sqrt{3}} - 3\sqrt{3}$

rationalizing the denominators and simplifying gives
$-\frac{17}{6} + \frac{\sqrt2}{6} - 3\sqrt2 - \frac{\sqrt{3}}{9} - 3\sqrt{3}$