Với \(x \ge 0,\,\,\,x \ne 4\) ta có:

\(\begin{array}{l}P = \dfrac{1}{{\sqrt x - 2}} + \dfrac{1}{{\sqrt x + 2}} - \dfrac{4}{{x - 4}}\\ = \dfrac{1}{{\sqrt x - 2}} + \dfrac{1}{{\sqrt x + 2}} - \dfrac{4}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ = \dfrac{{\sqrt x + 2 + \sqrt x - 2 - 4}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ = \dfrac{{2\sqrt x - 4}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\ = \dfrac{{2\left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}} = \dfrac{2}{{\sqrt x + 2}}\end{array}\)