Đáp án:
BPT $\leftrightarrow \frac{3}{x-1}+\frac{x-2}{5x-3}\le 0\leftrightarrow \frac{3(5x-3)+(x-1)(x-2)}{(x-1)(5x-3)}\le 0\leftrightarrow \frac{{{x}^{2}}+12x-7}{(x-1)(5x-3)}\le 0$
${{x}^{2}}+12x-7=0$ có 2 nghiệm ${{x}_{1,2}}=-6\pm \sqrt{43}$. Ta lập bảng xét dấu:
$\frac{{{x}^{2}}+12x-7}{(x-1)(5x-3)}\le 0\leftrightarrow \left[ \begin{align}& -6-\sqrt{43}\le x\le -6+\sqrt{43} \\& \frac{3}{5}<x<1 \\\end{align} \right.$
