Phương pháp giải:

Quy đồng và rút gọn biểu thức.

Lời giải chi tiết:

\(\begin{array}{l}P = \left( {\frac{{\sqrt x  + 1}}{{\sqrt x  - 1}} + \frac{{\sqrt x }}{{2 + \sqrt x }} - \frac{{4x + 2\sqrt x  - 4}}{{x - 4}}} \right)\left( {\frac{2}{{2 - \sqrt x }} - \frac{{\sqrt x  + 3}}{{2\sqrt x  - x}}} \right)\\P = \frac{{\left( {\sqrt x  + 1} \right)\left( {x - 4} \right) + \sqrt x \left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right) - \left( {4x + 2\sqrt x  - 4} \right)\left( {\sqrt x  - 1} \right)}}{{\left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}.\frac{{2\sqrt x  - \left( {\sqrt x  + 3} \right)}}{{\sqrt x \left( {2 - \sqrt x } \right)}}\\P = \frac{{\left( {x\sqrt x  + x - 4\sqrt x  - 4} \right) + \left( {x\sqrt x  - 3x + 2\sqrt x } \right) - \left( {4x\sqrt x  - 2x - 6\sqrt x  + 4} \right)}}{{\left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}.\frac{{\sqrt x  - 3}}{{\sqrt x \left( {2 - \sqrt x } \right)}}\\P = \frac{{ - 2x\sqrt x  + 4\sqrt x  - 8}}{{\left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}.\frac{{\sqrt x  - 3}}{{\sqrt x \left( {2 - \sqrt x } \right)}}\\P = \frac{{ - 2.\left( {x\sqrt x  + 8 - 2\sqrt x  - 4} \right)}}{{\left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}.\frac{{\sqrt x  - 3}}{{\sqrt x \left( {2 - \sqrt x } \right)}}\\P = \frac{{ - 2.\left[ {\left( {\sqrt x  + 2} \right)\left( {x - 2\sqrt x  + 4} \right) - 2\left( {\sqrt x  + 2} \right)} \right]}}{{\left( {\sqrt x  - 1} \right)\left( {\sqrt x  - 2} \right)\left( {\sqrt x  + 2} \right)}}.\frac{{\sqrt x  - 3}}{{\sqrt x \left( {2 - \sqrt x } \right)}}\\P = \frac{{2\left( {\sqrt x  + 2} \right)\left( {x - 2\sqrt x  + 2} \right)\left( {\sqrt x  - 3} \right)}}{{\sqrt x \left( {\sqrt x  - 1} \right){{\left( {\sqrt x  - 2} \right)}^2}\left( {\sqrt x  + 2} \right)}}\\P = \frac{{2\left( {x - 2\sqrt x  + 2} \right)\left( {\sqrt x  - 3} \right)}}{{\sqrt x \left( {\sqrt x  - 1} \right){{\left( {\sqrt x  - 2} \right)}^2}}}\end{array}\)