An inequality derived from an olympiad one

Question

This problem is a kind of complement of this.

Let $a,b,x,y,z\gt 0$, prove

$$\frac{x+y+z}{a+b}\ge \frac{xy^3}{ax^3+by^3}+\frac{yz^3}{ay^3+bz^3}+\frac{zx^3}{az^3+bx^3}$$

I have verified that this inequality is valid by computer and a lot of particular $(a, b, x, y, z)$ but I could not yet find a non-sophisticated proof.

Answer 1

It's wrong.

Try $(a,b,x,y,z)=(2,1,3,1,2).$

But it seems that it's true for $0< a\leq b$