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In a Delta ABC, points E and F divide si...

In a `Delta ABC,` points E and F divide sides AC and AB respectively so that `(AE)/(EC)=4 and (AF)/(FB)=1.` Suppose D is a point on side BC. Let G be the intersection of EF and AD and suppose D is situated so that `(AG)/(GD)=3/2.` If the ratio `(BD)/(DC)=a/b,` where a and b are in their lowest form, find the value of `(a + b).`

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