Giải thích các bước giải:
a,
Ta có:
\(\begin{array}{l}
P = \frac{{x - \sqrt x }}{{x - 9}} + \frac{1}{{\sqrt x + 3}} - \frac{1}{{\sqrt x - 3}}\\
= \frac{{x - \sqrt x }}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}} + \frac{{\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}} - \frac{{\sqrt x + 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \frac{{x - \sqrt x + \sqrt x - 3 - \sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \frac{{x - \sqrt x - 6}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \frac{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\
= \frac{{\sqrt x + 2}}{{\sqrt x + 3}}
\end{array}\)
b,
\[\begin{array}{l}
x = \frac{1}{{\sqrt 5 - 2}} + \frac{1}{{\sqrt 5 + 2}} = \frac{{\sqrt 5 + 2 + \sqrt 5 - 2}}{{\left( {\sqrt 5 - 2} \right)\left( {\sqrt 5 + 2} \right)}} = 2\sqrt 5 \\
P = \frac{{\sqrt x + 2}}{{\sqrt x + 3}} = \frac{{\sqrt {2\sqrt 5 } + 2}}{{\sqrt {2\sqrt 5 } + 3}}
\end{array}\]
