Đáp án: $M = \dfrac{{x + \sqrt x }}{{3\sqrt x - 1}}$
Giải thích các bước giải:
$\begin{array}{l}
B4)\\
Dkxd:x \ge 0;x\# \dfrac{1}{9}\\
M = \left( {\dfrac{{\sqrt x - 1}}{{3\sqrt x - 1}} - \dfrac{1}{{3\sqrt x + 1}} + \dfrac{{8\sqrt x }}{{9x - 1}}} \right)\\
:\left( {1 - \dfrac{{3\sqrt x - 2}}{{3\sqrt x + 1}}} \right)\\
= \dfrac{{\left( {\sqrt x - 1} \right)\left( {3\sqrt x + 1} \right) - \left( {3\sqrt x - 1} \right) + 8\sqrt x }}{{\left( {3\sqrt x + 1} \right)\left( {3\sqrt x - 1} \right)}}\\
:\dfrac{{3\sqrt x + 1 - 3\sqrt x + 2}}{{3\sqrt x + 1}}\\
= \dfrac{{3x - 2\sqrt x - 1 - 3\sqrt x + 1 + 8\sqrt x }}{{\left( {3\sqrt x + 1} \right)\left( {3\sqrt x - 1} \right)}}.\dfrac{{3\sqrt x + 1}}{3}\\
= \dfrac{{3x + 3\sqrt x }}{{3\sqrt x - 1}}.\dfrac{1}{3}\\
= \dfrac{{x + \sqrt x }}{{3\sqrt x - 1}}
\end{array}$
