Cauchy-Schwarz: Problema 10

Prove that for all \(a,b,c,x,y,z >0\) we have the following inequality: $$\frac{a}{b+c} (y+z) + \frac{b}{c+a}(z+x)+ \frac{c}{a+b}(x+y)
\geq 3 \cdot \frac{xy+yz+zx}{x+y+z}.$$

Walther Janous, Crux Mathematicorum