a+b

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In rectangle \(ABCD\), \(AB=6\), \(AD=30\), and \(G\) is the midpoint of \(AD\). Segment \(AB\) is extended \(2\) units beyond \(B\) to point \(E\), and \(F\) is the intersection of \(ED\) and \(BC\). If the area of \(BFDG\) can be expressed in the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime, positive integers, what is \(a+b\)?

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