Let $a;b;c>0$. Prove : $\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{c^{2}}{a+b}\geq \frac{b^{2}}{b+c}+\frac{c^{2}}{c+a}+\frac{a^{2}}{a+b}$ Let $a;b;c>0$. Prove :
$\frac{a^{2}}{b+c}+\frac{b^{2}}{c+a}+\frac{c^{2}}{a+b}\geq \frac{b^{2}}{b+c}+\frac{c^{2}}{c+a}+\frac{a^{2}}{a+b}$ 
P/s : Only use AM-GM and Cauchy-Schwarz
In the cases only use AM-GM and Cauchy-Schwarz; i don't have any thoughts about this problem !!

We need to prove that $$\sum\limits_{cyc}\frac{a^2-b^2}{b+c}\geq0$$ or $$\sum\limits_{cyc}(a^2-b^2)(a+b)(a+c)\geq0$$ or
$$\sum\limits_{cyc}(a^2-b^2)(a^2+ab+ac+bc)\geq0$$ or
$$\sum\limits_{cyc}(a^2-b^2)a^2\geq0$$ or
$$\sum\limits_{cyc}\left(\frac{a^4+b^4}{2}-a^2b^2\right)\geq0,$$
which is true by AM-GM.
