# Switching some Variables

Algebra Level 5

Given four reals $$(a,b,c,d)$$. If $$\dfrac{(a-b)(c-d)}{(b-c)(d-a)} = -\dfrac{4}{7}$$, then the value of $$\dfrac{(a-c)(b-d)}{(a-b)(c-d)} = \dfrac{A}{B}$$, where $$A,$$ and $$B$$ are coprime positive integer. If the value of $$\dfrac{A+B}{A-B} = \dfrac{C}{D}$$, where $$C,$$ and $$D$$ are coprime positive integer, find $$A+B+C+D$$.

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