Simplify the expression \[\frac{1}{\sqrt{36} + \sqrt{27}} + \frac{1}{\sqrt{27} + \sqrt{18}} + \frac{1}{\sqrt{18} + \sqrt{9}}.\]

\(\frac{1}{\sqrt{36} + \sqrt{27}} + \frac{1}{\sqrt{27} + \sqrt{18}} + \frac{1}{\sqrt{18} + \sqrt{9}}\)= \(\frac{1}{6+3\sqrt{3}}+\frac{1}{3\sqrt{3}+3\sqrt{2}}+\frac{1}{3\sqrt{2}+3}\)= \(\frac{1}{3}\)

Thanks! It was a big help!