For positive numbers $a,b,c$ that $a+b+c=3$ prove that: For positive numbers $a,b,c$ that $a+b+c=3$ prove that:
$\frac{a(a+b-2c)}{ab+1}+\frac{b(b+c-2a)}{bc+1}+\frac{c(c+a-2b)}{ac+1} \ge 0$
This problem wad in the first part of the inequality book(AM-GM inequality)But it doesn't seem to have a solution by AM_GM inequality since we have negative parantheses.Any hints?

C0nsider $(1.2,1.2,0.6)$ one has $LHS = \frac{1.2^2}{1.2^2 + 1} + \frac{-0.6\times 1.2}{1.2\times 0.6 + 1} + \frac{- 0.6\times 0.6}{1.2\times 0.6 + 1} < 0.$
