Solve for x
\left\{\begin{matrix}x>-\frac{2m-3}{\left(m-2\right)\left(m-1\right)}\text{, }&m<1\text{ or }m>2\\x\in \mathrm{R}\text{, }&m=2\\x<-\frac{2m-3}{\left(m-2\right)\left(m-1\right)}\text{, }&m>1\text{ and }m<2\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m\in \left(\frac{\sqrt{x^{2}+4}+3x-2}{2x},-\frac{\sqrt{x^{2}+4}-3x+2}{2x}\right)\text{, }&x<0\\m>\frac{3}{2}\text{, }&x=0\\m\in \left(\frac{\sqrt{x^{2}+4}+3x-2}{2x},\infty\right)\cup \left(-\infty,-\frac{\sqrt{x^{2}+4}-3x+2}{2x}\right)\text{, }&x>0\end{matrix}\right.
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