An algebra problem by Sai Venkatesh

Algebra Level 2

Given that a,ba,b and cc are real numbers such that a+b+c=0a+b+c=0, compute 1b2+c2a2+1c2+a2b2+1a2+b2c2.\frac { 1 }{ { b }^{ 2 }+{ c }^{ 2 }-{ a }^{ 2 } } +\frac { 1 }{ { c }^{ 2 }+{ a }^{ 2 }-{ b }^{ 2 } } +\frac { 1 }{ { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }.

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