CAPS 1996 Problem 6

The points $E$ and $D$ lie in the interior of sides $AC$ and $BC$ , respectively, of a triangle $ABC$ . Let $F$ be the intersection of the lines $AD$ and $BE$ .Show that the area of the traingles $ABC$ and $ABF$ satisfies:

$\frac{S_{ABC}}{S_{ABF}} = \frac{\mid{AC}\mid}{\mid{AE} \mid} + \frac{\mid{BC}\mid}{\mid{BD}\mid} - 1$ .