Solve the following equation for Fx (No results with Matlab, Mathcad & Co)

Question

I have this equation and I want to solve it for $F_x$.

$K(Q,m,F_\text{x})=\frac{{F_\text{x}}^2\cdot\left(m-1\right)}{\sqrt{{\left(m\cdot{F_\text{x}}^2-1\right)}^2+{F_\text{x}}^2\cdot{\left({F_\text{x}}^2-1\right)}^2\cdot{\left(m-1\right)}^2 \cdot Q^2}}$

I can't get any results with the solving options from Matlab and Mathcad. The result is always $0$ (zero).

Do you have an idea?

Answer 1

My hint is that this is because the solution is $x=0$. I am not going to prove this. But asking Mathematica for

Plot[Table[f[x, m, q], {m, -2, 2}, {q, -2, 2}], {x, -5, 5}]

gives me the figure below. (For $m=1$ I think any $x\in\mathbb{R}\setminus\{-1,1\}$ solves your problem. But that is a special case.)