[จูกัดเหลียง]

Let $x,y,z>0$ such that $xy+yz+zx=xyz$
Prove $$\frac{x+2y-z}{z+x}+\frac{y+2z-x}{x+y}+\frac{z+2x-y}{y+z}\ge \frac{xyz}{x+y+z}$$