How to prove that $FC/FA + GC/GA= 0$ from this triangle problem?

Question

In triangle $ABC$, a transversal line intersects $AB$, $BC$, $CA$ at $D,E,F$ respectively.

$BS$ intersects $AC$ at $G$, where $S$ is the intersection of $AE$ and $CD$.

How to prove that

$$\frac{FC}{FA} + \frac{GC}{GA} = 0$$