\[\begin{array}{l}
A = \left[ {\frac{{\sqrt x - 2}}{{x - 1}} + \frac{1}{{{{\left( {\sqrt x + 1} \right)}^2}}}} \right].\frac{{{{\left( {x - 1} \right)}^2}}}{2}\\
dk:x \ge 0;x \ne 1\\
= \left[ {\frac{{\sqrt x - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}} + \frac{1}{{{{\left( {\sqrt x + 1} \right)}^2}}}} \right].\frac{{{{\left( {x - 1} \right)}^2}}}{2}\\
= \frac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right) + \sqrt x - 1}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}.\frac{{{{\left( {x - 1} \right)}^2}}}{2}\\
= \frac{{x + \sqrt x - 2\sqrt x - 2 + \sqrt x - 1}}{{\left( {x - 1} \right)\left( {\sqrt x + 1} \right)}}.\frac{{{{\left( {x - 1} \right)}^2}}}{2}\\
= \frac{{x - 3}}{{\sqrt x + 1}}.\frac{{x - 1}}{2}\\
= \frac{{\left( {x - 3} \right)\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{2\left( {\sqrt x + 1} \right)}}\\
= \frac{{\left( {x - 3} \right)\left( {\sqrt x - 1} \right)}}{2}\\
vay:A = \frac{{\left( {x - 3} \right)\left( {\sqrt x - 1} \right)}}{2}\left( {x \ge 0;x \ne 1} \right)
\end{array}\]