Fractions on a rectangle

Geometry Level 4

In the rectangle ABCDABCD below, EE lies on BCBC and FF lies on CDCD such that the area of 3 triangles CEFCEF, ABEABE, ADFADF are 3, 4 and 5, respectively. If BEBC+DFDC=ab\dfrac {BE}{BC}+\dfrac{DF}{DC}= \dfrac ab, where aa and bb are coprime positive integers, what is a+ba+b?

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