Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
A = \frac{{\left( {x - 2\sqrt x } \right)\left( {\sqrt x + 2} \right) + \left( {\sqrt x - 1} \right)\left( {\sqrt x + 2} \right) - 3\sqrt x \left( {\sqrt x - 2} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{x\sqrt x + 2x - 2x - 4\sqrt x + x + \sqrt x - 2 - 3x + 6\sqrt x }}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
= \frac{{x\sqrt x - 2x + 3\sqrt x }}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}\\
A = \left( {\frac{1}{{\sqrt x - 1}} + \frac{{\sqrt x }}{{x - 1}}} \right).\frac{{x - \sqrt x }}{{2\sqrt x + 1}} = \frac{{\sqrt x + 1 + \sqrt x }}{{x - 1}}.\frac{{\sqrt x \left( {\sqrt x - 1} \right)}}{{2\sqrt x + 1}}\\
= \frac{{\sqrt x }}{{\sqrt x + 1}}\\
M = \frac{{2\sqrt x + 2 + 2\sqrt x - 2 - 5 + \sqrt x }}{{x - 1}} = \frac{{5\sqrt x - 5}}{{x - 1}}\\
= \frac{5}{{\sqrt x + 1}}\\
A = \frac{1}{{x\sqrt x }} + \frac{1}{2} = \frac{{2 + x\sqrt x }}{{2x\sqrt x }}\\
A = \frac{{x + 3 + 2\sqrt x - 6 - \sqrt x - 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \frac{{x - \sqrt x - 6}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} = \frac{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \frac{{\sqrt x + 2}}{{\sqrt x + 3}}
\end{array}\)
