Đáp án:
$\begin{array}{l}
a)P = \frac{{2a + 4}}{{a\sqrt a - 1}} + \frac{{\sqrt a + 2}}{{a + \sqrt a + 1}} - \frac{2}{{\sqrt a - 1}}\\
= \frac{{2a + 4 + \left( {\sqrt a + 2} \right)\left( {\sqrt a - 1} \right) - 2\left( {a + \sqrt a + 1} \right)}}{{\left( {\sqrt a - 1} \right)\left( {a + \sqrt a + 1} \right)}}\\
= \frac{{2a + 4 + a + \sqrt a - 2 - 2a - 2\sqrt a - 2}}{{\left( {\sqrt a - 1} \right)\left( {a + \sqrt a + 1} \right)}}\\
= \frac{{a - \sqrt a }}{{\left( {\sqrt a - 1} \right)\left( {a + \sqrt a + 1} \right)}}\\
= \frac{{\sqrt a }}{{a + \sqrt a + 1}}\\
b)a = 3 - 2\sqrt 2 \left( {tmdk} \right)\\
\Rightarrow a = {\left( {\sqrt 2 - 1} \right)^2}\\
\Rightarrow \sqrt a = \sqrt 2 - 1\\
\Rightarrow P = \frac{{\sqrt 2 - 1}}{{3 - 2\sqrt 2 + \sqrt 2 - 1 + 1}}\\
= \frac{{\sqrt 2 - 1}}{{3 - \sqrt 2 }}\\
= \frac{{\left( {\sqrt 2 - 1} \right)\left( {3 + \sqrt 2 } \right)}}{{9 - 2}}\\
= \frac{{2\sqrt 2 - 1}}{7}
\end{array}$
