\(\begin{array}{l}
a)\,\,{m^2}x + 3mx + 1 = {m^2} - 2x\\
\Leftrightarrow \left( {{m^2} + 3m + 2} \right)x = {m^2} - 1\\
\Leftrightarrow \left( {m + 1} \right)\left( {m + 2} \right)x = \left( {m + 1} \right)\left( {m - 1} \right)\,\,\,\left( * \right)\\
+ )\,\,\,Voi\,\,\,m = - 1 \Rightarrow \left( * \right) \Leftrightarrow 0x = 0\\
\Rightarrow pt\,\,co\,\,\,vo\,\,so\,\,nghiem.\\
+ )\,\,Voi\,\,m = - 2 \Rightarrow \left( * \right) \Leftrightarrow 0x = 3\\
\Rightarrow pt\,\,vo\,\,nghiem.\\
+ )\,\,\,Voi\,\,\,\left\{ \begin{array}{l}
m \ne - 1\\
m \ne - 2
\end{array} \right. \Rightarrow \left( * \right) \Leftrightarrow \left( {m + 2} \right)x = m - 1 \Leftrightarrow x = \frac{{m - 1}}{{m + 2}}\\
\Rightarrow pt\,\,co\,\,nghiem\,\,duy\,\,nhat:\,\,x = \frac{{m - 1}}{{m + 2}}.\\
b)\,\,\,{m^2}\left( {x - 1} \right) + 3mx = \left( {{m^2} + 3} \right)x - 1\\
\Leftrightarrow {m^2}x - {m^2} + 3mx - \left( {{m^2} + 3} \right)x = - 1\\
\Leftrightarrow \left( {{m^2} + 3m - {m^2} - 3} \right) = {m^2} - 1\\
\Leftrightarrow 3\left( {m - 1} \right)x = \left( {m - 1} \right)\left( {m + 1} \right)\,\,\,\,\left( * \right)\\
+ )\,\,\,Voi\,\,\,m = 1 \Rightarrow \left( * \right) \Leftrightarrow 0x = 0\\
\Rightarrow pt\,\,co\,\,vo\,\,so\,\,nghiem.\\
+ )\,\,\,Voi\,\,m \ne 1 \Rightarrow \left( * \right) \Leftrightarrow 3x = m + 1 \Leftrightarrow x = \frac{{m + 1}}{3}\\
\Rightarrow pt\,\,co\,\,\,nghiem\,\,\,duy\,\,nhat\,\,\,x = \frac{{m + 1}}{3}.
\end{array}\)
