7. Let the area of parallelogram $ABCD$ be $S$, points $E, F$ are on $AB, AD$ respectively, and $EB=\frac{2}{m} AB$, $AF=\frac{3}{n} AD$ (where $m, n$ are natural numbers greater than 4). $BF$ intersects $CE$ at $G$. Find:
(1) The area of $\triangle BEG$,
(2) $EG: GC=$ ? , $BG: GF=$ ?
(1989, Hefei City Junior High School Competition)
$\begin{array}{c}\text { (Answer: } S \triangle \mathbf{B \mathbf { G }}=\frac{6 S}{m(m n+6)}, \\ E G: G C=6: m n, B G: G F=2 n:[n \\ \cdot(m-2)+6])\end{array}$