Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
P = \left( {\dfrac{{4\sqrt x }}{{\sqrt x + 2}} - \dfrac{{8x}}{{x - 4}}} \right):\left( {\dfrac{{\sqrt x - 1}}{{x - 2\sqrt x }} - \dfrac{2}{{\sqrt x }}} \right)\\
= \left( {\dfrac{{4\sqrt x }}{{\sqrt x + 2}} - \dfrac{{8x}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}} \right):\left( {\dfrac{{\sqrt x - 1}}{{\sqrt x \left( {\sqrt x - 2} \right)}} - \dfrac{2}{{\sqrt x }}} \right)\\
= \dfrac{{4\sqrt x \left( {\sqrt x - 2} \right) - 8x}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}:\dfrac{{\left( {\sqrt x - 1} \right) - 2\left( {\sqrt x - 2} \right)}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{4x - 8\sqrt x - 8x}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}:\dfrac{{\sqrt x - 1 - 2\sqrt x + 4}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{ - 4x - 8\sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}:\dfrac{{ - \sqrt x + 3}}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \dfrac{{ - 4.\sqrt x \left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x - 2} \right).\left( {\sqrt x + 2} \right)}}.\dfrac{{\sqrt x .\left( {\sqrt x - 2} \right)}}{{ - \sqrt x + 3}}\\
= \dfrac{{ - 4.{{\sqrt x }^2}}}{{ - \sqrt x + 3}}\\
= \dfrac{{4x}}{{\sqrt x - 3}}
\end{array}\)
