Explanation of differentiating implicit functions

Question

$F(x,y,z)=0$, where $F \in C^2$ in some neighborhood of point (a,b,c) in which $F(a,b,c)\neq 0$ For the constant function $(x,y)->F(x,y,f(x,y))$ based on $f'(x,y)=-(D_zF(x,y,z))^{-1}(D_xF(x,y,z),D_yF(x,y,z))$ we have $f_{x}={-{F_{x}\over F_{z}}}$ and $f_{y}={-{F_{y}\over F_{z}}}$ where these indexes indicate partial derivatives. I don't understand how this last conclusion is derived.