$\begin{array}{l} P = \left( {\dfrac{2}{{\sqrt 3 - 1}} + \dfrac{3}{{\sqrt 3 - 2}} + \dfrac{{15}}{{3 - \sqrt 3 }}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ P = \left( {\dfrac{{2\left( {\sqrt 3 + 1} \right)}}{{3 - 1}} + \dfrac{{3\left( {\sqrt 3 + 2} \right)}}{{3 - 4}} + \dfrac{{15\left( {3 + \sqrt 3 } \right)}}{{9 - 3}}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ P = \left( {\sqrt 3 + 1 - 3\left( {\sqrt 3 + 2} \right) + \dfrac{{15 + 5\sqrt 3 }}{2}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ P = \left( { - 2\sqrt 3 - 5 + \dfrac{{15 + 5\sqrt 3 }}{2}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ P = \left( {\dfrac{{15 + 5\sqrt 3 - 10 - 4\sqrt 3 }}{2}} \right).\dfrac{1}{{\sqrt 3 + 5}} = \dfrac{{5 + \sqrt 3 }}{2}.\dfrac{1}{{\sqrt 3 + 5}} = \dfrac{1}{2}\\ b)\left( {\dfrac{{\sqrt {14} - \sqrt 7 }}{{1 - \sqrt 2 }} + \dfrac{{\sqrt {15} - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\dfrac{1}{{\sqrt 7 - \sqrt 5 }}\\ = \left( {\dfrac{{\sqrt 7 \left( {\sqrt 2 - 1} \right)}}{{1 - \sqrt 2 }} + \dfrac{{\sqrt 5 \left( {\sqrt 3 - 1} \right)}}{{1 - \sqrt 3 }}} \right).\left( {\sqrt 7 - \sqrt 5 } \right)\\ = \left( { - \sqrt 7 - \sqrt 5 } \right).\left( {\sqrt 7 - \sqrt 5 } \right) = - \left( {\sqrt 7 - \sqrt 5 } \right)\left( {\sqrt 7 + \sqrt 5 } \right) = - \left( {7 - 5} \right) = - 2 \end{array}$
