Maximum Product of Sums

Algebra Level 4

If \(a, b\) and \(c \) are distinct, non-zero reals that satisfy \(a + b + c =0\) , what is the maximum of \[\left(\frac {a}{b-c} + \frac {b}{c-a} + \frac {c}{a-b} \right)\left( \frac {b-c}{a} + \frac {c-a}{b} + \frac {a-b}{c}\right)? \]

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