CEMC Euclid, 2007

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, line segment $FCG$ passes through vertex $C$ of square $ABCD$ , with $F$ lying on $AB$ extended and $G$ lying on $AD$ extended. Prove that $\frac{1}{AB}=\frac{1}{AF}+\frac{1}{AG}$ .

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