$\begin{array}{l} \dfrac{4}{{\sqrt 3 - 1}} + \dfrac{7}{{3 - \sqrt 2 }} - 2\sqrt 3 \\ = \dfrac{{4\left( {\sqrt 3 + 1} \right)}}{{3 - 1}} + \dfrac{{7\left( {3 + \sqrt 2 } \right)}}{{9 - 2}} - 2\sqrt 3 \\ = 2\left( {\sqrt 3 + 1} \right) + 3 + \sqrt 2 - 2\sqrt 3 \\ = 5 + \sqrt 2 \end{array}$
