$\begin{array}{l} P = \left( {\sqrt x - \dfrac{1}{{\sqrt x }}} \right):\left( {\dfrac{{\sqrt x - 1}}{{\sqrt x }} + \dfrac{{1 - \sqrt x }}{{x + \sqrt x }}} \right)\\ P = \left( {\dfrac{{x - 1}}{{\sqrt x }}} \right):\dfrac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right) + 1 - \sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}\\ P = \dfrac{{x - 1}}{{\sqrt x }}.\dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{x - \sqrt x }}\\ = \dfrac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right).\sqrt x \left( {\sqrt x + 1} \right)}}{{x\left( {\sqrt x - 1} \right)}}\\ = \dfrac{{{{\left( {\sqrt x + 1} \right)}^2}}}{{\sqrt x }}\\ b)P = \dfrac{{{{\left( {\sqrt x + 1} \right)}^2}}}{{\sqrt x }}\\ = \dfrac{{x + 2\sqrt x + 1}}{{\sqrt x }}\\ = \sqrt x + 2 + \dfrac{1}{{\sqrt x }} \ge 2\sqrt {\sqrt x .\dfrac{1}{{\sqrt x }}} + 2 = 4 > 2 \end{array}$
