Solve f^2x=3x/x^2-1

$$f ^ { 2 } x = \frac { 3 x } { x ^ { 2 } - 1 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\sqrt{3}\left(x^{2}-1\right)^{-\frac{1}{2}}\text{; }f=\sqrt{3}\left(x^{2}-1\right)^{-\frac{1}{2}}\text{, }&x\neq -1\text{ and }x\neq 1\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\sqrt{1+\frac{3}{f^{2}}}\text{; }x=\sqrt{1+\frac{3}{f^{2}}}\text{, }&f\neq 0\end{matrix}\right.$$

Solve for f

$$\left\{\begin{matrix}f=\sqrt{\frac{3}{x^{2}-1}}\text{; }f=-\sqrt{\frac{3}{x^{2}-1}}\text{, }&|x|>1\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{f^{2}+3}}{|f|}\text{; }x=-\frac{\sqrt{f^{2}+3}}{|f|}\text{, }&f\neq 0\end{matrix}\right.$$