For $a,b,c >0$ prove that :
$$\frac{a}{(b+c)^4}+\frac{b}{(c+a)^4}+\frac{c}{(a+b)^4} \geq \frac{3}{2(a+b)(b+c)(c+a)}.$$
I don't know how should I start. It is difficult for me because the denominators has the power equals with 4, I think it must decrease the rank of the power.
danke :)