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ab+bc+ca=0
ab+bc = -ca
Or ab+ca= -bc
Or bc+ca = -ab
Now
1/(a^2 -bc) + 1/(b^2 -ca) + 1/(c^2 -ab)
= 1/(a^2 +ab+ca) +1/(b^2 +ab+bc) +1/(c^2 +bc+ca)
= 1/(a+b+c) * (1/a + 1/b + 1/c)
= 1/(a+b+c) * (bc + ca + ab)/abc
= (ab+bc+ca)/(a+b+c) abc
= (a+b+c) abc/(a+b+c) abc
=0
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