Partial Derivatives - Differentials

[elspanel]

Hi everyone!

i've stuck in this problem which says
if f(x/z, -z/y )=0 with z=φ(x,y) then i prove that x/z*∂z/∂x + y/z*∂z/∂y = 1

How can i use the z=f(x,y) function?

I started my solution from this point

∂z/dx=∂f/dx

∂z/∂y = ∂f/∂y

Could this be a solution way when we have envolved functions?can somebody help me??
Thank you