# stability in odes – Finding all equilibrium points of a differential system

So, I want to find all equilibrium points of the next differential system

begin{align*} x’ &= ,gz – hx\ y’ &= , frac{c}{a+bx}+ky\ z’ &= ey – fz end{align*}

And I know I can write it as:
$$begin{pmatrix} h & 0 & g\ ? & k & 0\ 0 & e & f end{pmatrix}$$
But I don’t know what to do with the $$frac{c}{a+bx}$$ (hence the ? in the matrix).

I also tried to make them all equal to zero and I ended up with the next problem:

$$x=frac{g}{h}z$$ and $$y=frac{f}{e}zimplies frac{c}{a+frac{bgz}{h}}=frac{kfz}{e}$$. And finding z in there is a nightmare.

It would be great I you could give me any insight.