Đáp án:
$\begin{array}{l}
P = \left( {\frac{{\sqrt x - 4}}{{\sqrt x \left( {\sqrt x - 2} \right)}} + \frac{3}{{\sqrt x - 2}}} \right):\left( {\frac{{\sqrt x + 2}}{{\sqrt x }} - \frac{{\sqrt x }}{{\sqrt x - 2}}} \right)\\
a)Đkxđ:x > 0;x \ne 4\\
P = \frac{{\sqrt x - 4 + 3.\sqrt x }}{{\sqrt x \left( {\sqrt x - 2} \right)}}:\frac{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right) - \sqrt x .\sqrt x }}{{\sqrt x \left( {\sqrt x - 2} \right)}}\\
= \frac{{4\sqrt x - 4}}{{\sqrt x \left( {\sqrt x - 2} \right)}}.\frac{{\sqrt x \left( {\sqrt x - 2} \right)}}{{x - 4 - x}}\\
= \frac{{4\left( {\sqrt x - 1} \right)}}{{ - 4}}\\
= 1 - \sqrt x \\
b)x = 6 - 2\sqrt 5 \left( {tmdk} \right)\\
\Rightarrow x = 5 - 2\sqrt 5 + 1 = {\left( {\sqrt 5 - 1} \right)^2}\\
\Rightarrow \sqrt x = \left| {\sqrt 5 - 1} \right| = \sqrt 5 - 1\\
\Rightarrow P = 1 - \sqrt x = 1 - \left( {\sqrt 5 - 1} \right) = 2 - \sqrt 5 \\
Vậy\,P =2 - \sqrt 5 \,khi\,x = 6 - 2\sqrt 5
\end{array}$
