Rút gọn biểu thức: P = ( $\frac{(căn x) – 1}{(3 căn x)-1}$ – $\frac{1}{(3 căn x) + 1}$ + $\frac{8 căn x}{9x – 1}$ ) : (1 – $\frac{(3 căn x) – 2}{(3 căn x) + 1}$ ).
Rút gọn biểu thức: P = ( $\frac{(căn x) – 1}{(3 căn x)-1}$ – $\frac{1}{(3 căn x) + 1}$ + $\frac{8 căn x}{9x – 1}$ ) : (1 – $\frac{(3 căn x) – 2}{(3 căn x) + 1}$ ).
Đáp án:
$\begin{array}{l}
Dkxd:\left\{ \begin{array}{l}
x \ge 0\\
x \ne \dfrac{1}{9}
\end{array} \right.\\
P = \left( {\dfrac{{\sqrt x – 1}}{{3\sqrt x – 1}} – \dfrac{1}{{3\sqrt x + 1}} + \dfrac{{8\sqrt x }}{{9x – 1}}} \right)\\
:\left( {1 – \dfrac{{3\sqrt x – 2}}{{3\sqrt x + 1}}} \right)\\
= \dfrac{{\left( {\sqrt x – 1} \right)\left( {3\sqrt x + 1} \right) – 3\sqrt x + 1 + 8\sqrt x }}{{\left( {3\sqrt x – 1} \right)\left( {3\sqrt x + 1} \right)}}:\\
\dfrac{{3\sqrt x + 1 – 3\sqrt x + 2}}{{3\sqrt x + 1}}\\
= \dfrac{{3x – 2\sqrt x – 1 + 5\sqrt x + 1}}{{\left( {3\sqrt x – 1} \right)\left( {3\sqrt x + 1} \right)}}.\dfrac{{3\sqrt x + 1}}{3}\\
= \dfrac{{3x + 3\sqrt x }}{{3\sqrt x – 1}}.\dfrac{1}{3}\\
= \dfrac{{x + \sqrt x }}{{3\sqrt x – 1}}
\end{array}$