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$.