$\begin{array}{l} P = \left( {\dfrac{{\sqrt x - 2}}{{x - 1}} - \dfrac{{\sqrt x + 2}}{{x + 2\sqrt x + 1}}} \right){\left( {\dfrac{{1 - x}}{{\sqrt 2 }}} \right)^2}\\ P = \left[ {\dfrac{{\sqrt x - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}} - \dfrac{{\sqrt x + 2}}{{{{\left( {\sqrt x + 1} \right)}^2}}}} \right].\dfrac{{{{\left( {1 - x} \right)}^2}}}{2}\\ P = \dfrac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right) - \left( {\sqrt x + 2} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}.\dfrac{{{{\left( {1 - x} \right)}^2}}}{2}\\ P = \dfrac{{x - \sqrt x - 2 - x - \sqrt x + 2}}{{\left( {x - 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{{{\left( {1 - x} \right)}^2}}}{2}\\ P = \dfrac{{ - 2\sqrt x }}{{\sqrt x + 1}}.\dfrac{{x - 1}}{2} = \dfrac{{ - \sqrt x \left( {x - 1} \right)}}{{\sqrt x + 1}}\\ P = \dfrac{{ - \sqrt x \left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x + 1}} = - \sqrt x \left( {\sqrt x - 1} \right)\\ = \sqrt x - x \end{array}$
