Solve x/-x-3-2=m^2/x-3

$$\frac { x } { - x - 3 } - 2 = \frac { m ^ { 2 } } { x - 3 }$$

Solve for m (complex solution)

$$m=-i\left(x+3\right)^{-\frac{1}{2}}\sqrt{3\left(x-3\right)}\sqrt{x+2}$$

$$m=i\left(x+3\right)^{-\frac{1}{2}}\sqrt{3\left(x-3\right)}\sqrt{x+2}\text{, }x\neq -3\text{ and }x\neq 3$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{\sqrt{m^{4}-42m^{2}+225}}{6}-\frac{m^{2}}{6}+\frac{1}{2}\text{, }&\text{unconditionally}\\x=\frac{\sqrt{m^{4}-42m^{2}+225}}{6}-\frac{m^{2}}{6}+\frac{1}{2}\text{, }&m\neq 0\end{matrix}\right.$$

Solve for m

$$m=\sqrt{\frac{3\left(3-x\right)\left(x+2\right)}{x+3}}$$

$$m=-\sqrt{\frac{3\left(3-x\right)\left(x+2\right)}{x+3}}\text{, }\left(x\geq -2\text{ and }x<3\right)\text{ or }x<-3$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{m^{4}-42m^{2}+225}}{6}-\frac{m^{2}}{6}+\frac{1}{2}\text{, }&|m|\geq \sqrt{3}+3\sqrt{2}\text{ or }|m|\leq 3\sqrt{2}-\sqrt{3}\\x=\frac{\sqrt{m^{4}-42m^{2}+225}}{6}-\frac{m^{2}}{6}+\frac{1}{2}\text{, }&\left(|m|\leq 3\sqrt{2}-\sqrt{3}\text{ and }m\neq 0\right)\text{ or }|m|\geq \sqrt{3}+3\sqrt{2}\end{matrix}\right.$$