Rút gọn biểu thức \(A = \left( {\frac{{x + 2}}{{\sqrt x + 1}} - \sqrt x } \right):\left( {\frac{{\sqrt x - 4}}{{1 - x}} - \frac{{\sqrt x }}{{\sqrt x + 1}}} \right)\).

Ta có \(A = \left( {\frac{{x + 2}}{{\sqrt x + 1}} - \sqrt x } \right):\left( {\frac{{\sqrt x - 4}}{{1 - x}} - \frac{{\sqrt x }}{{\sqrt x + 1}}} \right)\)

\( = \frac{{x + 2 - \sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x + 1}}:\frac{{\sqrt x - 4 - \sqrt x \left( {1 - \sqrt x } \right)}}{{\left( {1 - \sqrt x } \right)\left( {1 + \sqrt x } \right)}}\)

\( = \frac{{x + 2 - x - \sqrt x }}{1}.\frac{{1 - \sqrt x }}{{\sqrt x - 4 - \sqrt x + x}}\)

\[ = \frac{{\left( {2 - \sqrt x } \right)\left( {1 - \sqrt x } \right)}}{{x - 4}} = \frac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}} = \frac{{\sqrt x - 1}}{{\sqrt x + 2}}\].