For all positive numbers $a,b,c$, prove that $$\frac{a^3}{b^2-bc+c^2}+\frac{b^3}{a^2-ac+c^2}+\frac{c^3}{a^2-ab+b^2}\geq 3 \frac{(ab+bc+ac)}{a+b+c}$$
Note that both side are homogeneous of degree 1, so I think it is safe to assume $a+b+c=1$ but this does not go very far.
Any ideas/hint? Thanks