ĐKXĐ: \(x\ne-2\)
\(\Leftrightarrow\left|3x-1\right|=\left|x-3\right|\left(x+2\right)\)
- Với \(x\ge3\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)-\left(3x-1\right)=0\)
\(\Leftrightarrow x^2-4x-5=0\Rightarrow\left[{}\begin{matrix}x=-1\left(l\right)\\x=5\end{matrix}\right.\)
- Với \(\frac{1}{3}< x< 3\)
\(\Leftrightarrow3x-1=\left(3-x\right)\left(x+2\right)\)
\(\Leftrightarrow x^2+2x-7=0\Rightarrow\left[{}\begin{matrix}x=-1+2\sqrt{2}\\x=-1-2\sqrt{2}\left(l\right)\end{matrix}\right.\)
- Với \(x\le\frac{1}{3}\)
\(\Leftrightarrow1-3x=\left(3-x\right)\left(x+2\right)\)
\(\Leftrightarrow x^2-4x-5=0\Rightarrow\left[{}\begin{matrix}x=-1\\x=5\left(l\right)\end{matrix}\right.\)
