Given a $\triangle ABC$ with the side lengths $BC=a,\ CA=b,\ AB=c$.
Prove that :
$$\displaystyle \frac{a^2+b^2-c^2}{a+b-c}+\frac{b^2+c^2-a^2}{b+c-a}+\frac{c^2+a^2-b^2}{c+a-b}\le a+b+c$$

http://suseum.jp/gq/question/1852