Prove that $a/(p-a) + b/(p-b) + c/(p-c) \ge 6$ Prove that $a/(p-a) + b/(p-b) + c/(p-c) \ge 6$ , where $a,b,c$ are the sides of a triangle and $p$ is the semi-perimeter .

By C-S $\sum\limits_{cyc}\frac{a}{p-a}\geq\frac{(a+b+c)^2}{\sum\limits_{cyc}(pa-a^2)}=\frac{2(a+b+c)^2}{(a+b+c)^2-2(a^2+b^2+c^2)}\geq\frac{2(a+b+c)^2}{(a+b+c)^2-\frac{2}{3}(a+b+c)^2}=6$
