Đáp án:
\(\left[ \begin{array}{l}
x = \dfrac{6}{5}\\
x = 6
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ {0;3} \right\}\\
Pt \to \left| {\dfrac{{3x}}{{2x - 6}}} \right| = 2 + \left| {\dfrac{{2x - 6}}{x}} \right|\\
\to \dfrac{{9{x^2}}}{{4{x^2} - 24x + 36}} = 4 + \dfrac{{4{x^2} - 24x + 36}}{{{x^2}}} + 4.\dfrac{{2x - 6}}{x}\\
\to \dfrac{{9{x^2}}}{{4{x^2} - 24x + 36}} = \dfrac{{4{x^2} - 24x + 36 + 4{x^2} + 8{x^2} - 24x}}{{{x^2}}}\\
\to \dfrac{{9{x^2}}}{{4{x^2} - 24x + 36}} = \dfrac{{16{x^2} - 48x + 36}}{{{x^2}}}\\
\to 9{x^4} = 64{x^4} - 384{x^3} + 576{x^2} - 192{x^3} + 1152{x^2} - 1728x + 144{x^2} - 864x + 1296\\
\to 55{x^4} - 576{x^3} + 1872{x^2} - 2592x + 1296 = 0\\
\to 55{x^4} - 66{x^3} - 510{x^3} + 612{x^2} + 1260{x^2} - 1512x - 1080x + 1296 = 0\\
\to 11{x^3}\left( {5x - 6} \right) - 102{x^2}\left( {5x - 6} \right) + 252x\left( {5x - 6} \right) - 216\left( {5x - 6} \right) = 0\\
\to \left[ \begin{array}{l}
5x - 6 = 0\\
11{x^3} - 102{x^2} + 252x - 216 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{6}{5}\\
x = 6
\end{array} \right.
\end{array}\)
