Đáp án: x=2 hoặc x=6
Giải thích các bước giải:
$\begin{array}{l}
Dkxd:x \ne 3;x \ne 0\\
\left| {\dfrac{{3x}}{{2x - 6}}} \right| - \left| {\dfrac{{2x - 6}}{x}} \right| = 2\\
\Rightarrow 3.\left| {\dfrac{x}{{2x - 6}}} \right| - \left| {\dfrac{{2x - 6}}{x}} \right| = 2\\
Đặt:\left| {\dfrac{x}{{2x - 6}}} \right| = t\left( {t > 0} \right)\\
\Rightarrow \left| {\dfrac{{2x - 6}}{x}} \right| = \dfrac{1}{t}\\
\Rightarrow 3.t - \dfrac{1}{t} = 2\\
\Rightarrow 3{t^2} - 2t - 1 = 0\left( {do:t > 0} \right)\\
\Rightarrow \left( {3t + 1} \right)\left( {t - 1} \right) = 0\\
\Rightarrow t = 1\left( {do:t > 0} \right)\\
\Rightarrow \left| {\dfrac{x}{{2x - 6}}} \right| = 1\\
\Rightarrow \left[ \begin{array}{l}
\dfrac{x}{{2x - 6}} = 1\\
\dfrac{x}{{2x - 6}} = - 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 2x - 6\\
x = - 2x + 6
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 6\left( {tmdk} \right)\\
x = 2\left( {tm} \right)
\end{array} \right.
\end{array}$
Vậy x=2 hoặc x=6
