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