Đáp án:
$\begin{array}{l}
2)a){m^2}\left( {x - 1} \right) = mx - 1\\
\Rightarrow {m^2}x - mx = {m^2} - 1\\
\Rightarrow \left( {{m^2} - m} \right)x = {m^2} - 1\\
Pt\,có\,nghiệm \Leftrightarrow {m^2} - m \ne 0 \Rightarrow \left\{ \begin{array}{l}
m \ne 0\\
m \ne 1
\end{array} \right.\\
b)\frac{3}{{x - 1}} = m\,\\
Có\,nghiệm \Leftrightarrow m \ne 0\\
3)\\
a)\frac{{2m - 1}}{{x - 2}} = m - 3\\
\Rightarrow 2m - 1 = \left( {m - 3} \right)\left( {x - 2} \right)\\
\Rightarrow 2m - 1 = \left( {m - 3} \right)x - 2m + 6\\
\Rightarrow \left( {m - 3} \right)x = 4m - 7\\
Pt\,có\,nghiệm\,duy\,nhất\\
\Leftrightarrow \left\{ \begin{array}{l}
m - 3 \ne 0\\
4m - 7 \ne 0\\
\left( {m - 3} \right).2 \ne 4m - 7
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
m \ne 3\\
m \ne \frac{7}{4}\\
2m - 6 \ne 4m - 7
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
m \ne 3\\
m \ne \frac{7}{4}\\
m \ne \frac{1}{2}
\end{array} \right.
\end{array}$
