$\begin{array}{l} a)\left( {\dfrac{{15}}{{\sqrt 6 + 1}} + \dfrac{4}{{\sqrt 6 - 2}} - \dfrac{{12}}{{3 - \sqrt 6 }}.} \right)\left( {\sqrt 6 + 11} \right)\\ = \left( {\dfrac{{15\left( {\sqrt 6 - 1} \right)}}{{6 - 1}} + \dfrac{{4\left( {\sqrt 6 + 2} \right)}}{{6 - 4}} - \dfrac{{12\left( {3 + \sqrt 6 } \right)}}{{9 - 6}}} \right).\left( {\sqrt 6 + 11} \right)\\ = \left[ {3\left( {\sqrt 6 - 1} \right) + 2\left( {\sqrt 6 + 2} \right) - 4\left( {3 + \sqrt 6 } \right)} \right]\left( {\sqrt 6 + 11} \right)\\ = \left( {\sqrt 6 - 11} \right)\left( {\sqrt 6 + 11} \right)\\ = 6 - 121 = - 115 \end{array}$
