Đáp án:
$\begin{array}{l}
Dkxd:a \ge 0;a \ne 1\\
A = \frac{{a - 1}}{{\sqrt a + 1}} + \frac{{a - \sqrt a }}{{\sqrt a - 1}} + a + 2\\
= \frac{{\left( {\sqrt a + 1} \right)\left( {\sqrt a - 1} \right)}}{{\sqrt a + 1}} + \frac{{\sqrt a \left( {\sqrt a - 1} \right)}}{{\sqrt a - 1}} + a + 2\\
= \sqrt a - 1 + \sqrt a + a + 2\\
= a + 2\sqrt a + 1\\
= {\left( {\sqrt a + 1} \right)^2}
\end{array}$