a) ĐKXĐ: \(x\ge0,x\ne4\)
\(b)P = \dfrac{{\sqrt x + 1}}{{\sqrt x - 2}} + \dfrac{{2\sqrt x }}{{\sqrt x + 2}} + \dfrac{{2 + 5\sqrt x }}{{4 - x}}\\ P = \dfrac{{\sqrt x + 1}}{{\sqrt x - 2}} + \dfrac{{2\sqrt x }}{{\sqrt x + 2}} + \dfrac{{2 + 5\sqrt x }}{{\left( {\sqrt x + 2} \right)\left( {2 - \sqrt x } \right)}}\\ P = \dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x + 2} \right) + 2\sqrt x \left( {\sqrt x - 2} \right) - \left( {2 + 5\sqrt x } \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ P = \dfrac{{x + 3\sqrt x + 2 + 2x - 4\sqrt x - 2 - 5\sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ P = \dfrac{{3x - 6\sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ P = \dfrac{{3\sqrt x \left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ P = \dfrac{{3\sqrt x }}{{\sqrt x + 2}} \)
\(c)P=2\Rightarrow\)\(\dfrac{{3\sqrt x }}{{\sqrt x + 2}}=2 \)
\(\Leftrightarrow3\sqrt{x}=2\left(\sqrt{x}+2\right)\\ \Leftrightarrow3\sqrt{x}=2\sqrt{x}+4\\ \Leftrightarrow3\sqrt{x}-2\sqrt{x}=4\\ \Leftrightarrow\sqrt{x}=4\\ \Leftrightarrow x=16\)