$\begin{array}{l} P = \left( {\dfrac{{\sqrt x }}{{\sqrt x - 1}} - \dfrac{1}{{\sqrt x + 1}}} \right):\left( {\dfrac{1}{{\sqrt x + 1}} + \dfrac{2}{{x - 1}}} \right)\\ P = \dfrac{{\sqrt x \left( {\sqrt x + 1} \right) - \left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}:\left( {\dfrac{{\sqrt x - 1 + 2}}{{x - 1}}} \right)\\ P = \dfrac{{x + \sqrt x - \sqrt x + 1}}{{x - 1}}:\dfrac{{\sqrt x + 1}}{{x - 1}}\\ P = \dfrac{{x + 1}}{{\sqrt x + 1}}\\ b)\\ x = 4 - 2\sqrt 3 = {\left( {\sqrt 3 - 1} \right)^2}\\ \Rightarrow P = \dfrac{{4 - 2\sqrt 3 + 1}}{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} + 1}} = \dfrac{{5 - 2\sqrt 3 }}{{\sqrt 3 }} = \dfrac{{5\sqrt 3 - 6}}{3} \end{array}$
