Đáp án:
$\begin{array}{l}
\frac{1}{{\sqrt 3 }} + \frac{1}{{3\sqrt 2 }} + \frac{1}{{\sqrt 3 }}.\sqrt {\frac{5}{{12}} - \frac{1}{{\sqrt 6 }}} \\
= \frac{1}{{\sqrt 3 }} + \frac{1}{{3\sqrt 2 }} + \frac{1}{{\sqrt 3 }}.\sqrt {\frac{{5 - 2\sqrt 6 }}{{12}}} \\
= \frac{1}{{\sqrt 3 }} + \frac{1}{{3\sqrt 2 }} + \frac{1}{{\sqrt 3 }}.\frac{{\sqrt {{{\left( {\sqrt 3 - \sqrt 2 } \right)}^2}} }}{{2\sqrt 3 }}\\
= \frac{{2\sqrt 3 + 3\sqrt 2 + \sqrt 3 - \sqrt 2 }}{6}\\
= \frac{{3\sqrt 3 + 2\sqrt 2 }}{6}
\end{array}$
