Rút gọn biểu thức: \(A = \left( {\frac{{2x + 1}}{{x\sqrt x - 1}} - \frac{{\sqrt x }}{{x + \sqrt x + 1}}} \right).\left( {\frac{{1 + x\sqrt x }}{{1 + \sqrt x }} - \sqrt x } \right)\) với x ≥ 0; x ≠ 1.

\(A = \left( {\frac{{2x + 1}}{{x\sqrt x - 1}} - \frac{{\sqrt x }}{{x + \sqrt x + 1}}} \right).\left( {\frac{{1 + x\sqrt x }}{{1 + \sqrt x }} - \sqrt x } \right)\)

\[A = \left( {\frac{{2x + 1}}{{\left( {\sqrt x - 1} \right)\left( {x + \sqrt x + 1} \right)}} - \frac{{\sqrt x \left( {\sqrt x - 1} \right)}}{{\left( {x + \sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}} \right).\left( {\frac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{1 + \sqrt x }} - \sqrt x } \right)\]

\[A = \frac{{x + \sqrt x + 1}}{{\left( {\sqrt x - 1} \right)\left( {x + \sqrt x + 1} \right)}}.\left( {x - 2\sqrt x + 1} \right)\]

\[A = \frac{1}{{\sqrt x - 1}}.{\left( {\sqrt x - 1} \right)^2} = \sqrt x - 1\].