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(b+c)^2/3bc
multiply N and D by a
ab^2 + ac^2 + 2abc)/ 3abc
(c+a)^2/3ac
multiply N and D by b
bc^2 + ba^2 + 2abc)/3abc
( a+ b)^2/3ab
multiply N and D by c
ca^2 + cb^2 + 2cab )/ 3abc
Add
ab^2 + ac^2 + 2abc + Bc^2 + ba^2 + 2abc + ca^2 + cb^2 + 2cab)/3abc
ab^2+ ba^2 + ac^2 + ca^2 + bc^2 + cb^2 + 2abc +2abc + 2abc)/3abc
ab( b+ a) + ca( c+ a) + bc( c+ b) + 6abc)/3abc
As a+ b+ c= 0
a+ b= - c
b+ c= -a
c+ a= - b
So
ab( -c) + ca( -b) + bc( -a) + 6abc)/ 3abc
- abc - abc - abc + 6abc )/ 3abc
-3abc + 6abc)/3abc
3abc/3abc
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