KöMaL 2019 B5031

Let $F$ be a point on the extension of side $AD$ of parallelogram $ABCD$ beyond vertex $D$. Line segment $BF$ intersects side $CD$ at $G$ and diagonal $AC$ at $E$. Show that $\frac{1}{BE}=\frac{1}{BG}+\frac{1}{BF}$.