ĐKXĐ : \(\left\{\begin{matrix}x\ne\frac{1}{2}\\x\ne\frac{2}{3}\end{matrix}\right.\)
Ta có : \(\frac{3}{1-2x}>\frac{5}{3x-2}\Leftrightarrow\frac{3}{1-2x}-\frac{5}{3x-2}>0\)
\(\Leftrightarrow\frac{3\left(3x-2\right)-5\left(1-2x\right)}{\left(1-2x\right)\left(3x-2\right)}>0\Leftrightarrow\frac{\left(19x-11\right)}{\left(1-2x\right)\left(3x-2\right)}>0\)
\(\Leftrightarrow\left\{\begin{matrix}19x-11>0\\\left(1-2x\right)\left(3x-2\right)>0\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}19x-11< 0\\\left(1-2x\right)\left(3x-2\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x>\frac{11}{19}\\\frac{1}{2}< x< \frac{2}{3}\end{matrix}\right.\) (nhận) hoặc \(\left\{\begin{matrix}x< \frac{1}{2}\\\frac{1}{2}< x< \frac{2}{3}\end{matrix}\right.\) (loại)
\(\Leftrightarrow\frac{11}{19}< x< \frac{2}{3}\)
Vậy tập nghiệm của BPT : \(\left(\frac{11}{19};\frac{2}{3}\right)\)
