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.