ĐK: $x-1\ne 0\Leftrightarrow x\ne 1$
$\dfrac{2m-1}{x-1}=m-2$
$\Leftrightarrow (x-1)(m-2)=2m-1$
$\Leftrightarrow (m-2)x-(m-2)=2m-1$
$\Leftrightarrow (m-2)x=2m-1+m-2=3m-3$ $(*)$
* Nếu $m-2=0\Leftrightarrow m=2$:
$(*)\Leftrightarrow 0x=3$ (vô nghiệm)
* Nếu $m-2\ne 0\Leftrightarrow m\ne 2$
$(*)\Leftrightarrow x=\dfrac{3m-3}{m-2}$
$\dfrac{3m-3}{m-2}\ne 1$
$\Leftrightarrow 3m-3\ne m-2$
$\Leftrightarrow m\ne \dfrac{1}{2}$
Vậy:
Khi $m=2$ hoặc $m=\dfrac{1}{2}$, $S=\varnothing$
Khi $m\notin \{ \dfrac{1}{2}; 2\}$, $S=\Big\{ \dfrac{3m-3}{m-2}\Big\}$