Maximum Product of Sums

Algebra Level 4

If a,ba, b and cc are distinct, non-zero reals that satisfy a+b+c=0a + b + c =0 , what is the maximum of (abc+bca+cab)(bca+cab+abc)?\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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