Cho a, b, c >0 thỏa mãn ab+bc+ca=1. CMR: [tex]\frac{a-b}{1+c^2}+\frac{b-c}{1+a^2}+\frac{c-a}{1+b^2}=0[/tex]
[tex]\frac{a-b}{1+c^2}+\frac{b-c}{1+a^2}+\frac{c-a}{1+b^2}=\frac{a-b}{c^2+ab+bc+ca}+\frac{b-c}{a^2+ab+bc+ca}+\frac{c-a}{b^2+ab+bc+ca}=\frac{a-b}{(a+c)(c+b)}+\frac{b-c}{(a+b)(c+a)}+\frac{c-a}{(a+b)(c+b)}=\frac{1}{a+c}-\frac{1}{b+c}+\frac{1}{a+b}-\frac{1}{a+c}+\frac{1}{b+c}-\frac{1}{a+b}=0[/tex]