Let $a,b,c$ be positive real numbers. Prove that: $$ \frac{a^2+b^2}{a^2+ab} +\frac{b^2+c^2}{b^2+bc} +\frac{c^2+a^2}{c^2+ca} \ge \frac{9(a^2+b^2+c^2)}{(a+b+c)^2} $$
Similar problems: Advanced Olympiad Inequalities: Algebraic and Geometric Olympiad Inequalities
I've tried for Cauchy and A-GM, not much comes out