The following equation has a positive and a negative solution.

z-1/z+1 = 2/z+4
I need to find the positive solution,
any ideas please?

you probably meant ...

(z-1)/(z+1) = 2/(z+4)
cross-multiply
z^2 + 3z - 4 = 2z + 2
rearrange into a nice quadratic which factors very easily, one factor producing a positive, the other a negative solution.

let me know what you get.