Đáp án:
\( - x + \sqrt x \)
Giải thích các bước giải:
\(\begin{array}{l}
A = \dfrac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right) - \left( {\sqrt x + 2} \right)\left( {\sqrt x - 1} \right)}}{{\left( {x - 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{{{\left( {x - 1} \right)}^2}}}{2}\\
= \dfrac{{x - \sqrt x - 2 - x - \sqrt x + 2}}{{\left( {x - 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{{{\left( {x - 1} \right)}^2}}}{2}\\
= \dfrac{{ - 2\sqrt x }}{{\sqrt x + 1}}.\dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{2}\\
= - \sqrt x \left( {\sqrt x - 1} \right) = - x + \sqrt x
\end{array}\)
