with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$

Let $x,y,z\ge 0$, show that
$$\dfrac{y}{xy+2y+1}+\dfrac{z}{yz+2z+1}+\dfrac{x}{zx+2x+1}\le\dfrac{3}{4}$$

I had solve
$$\sum_{cyc}\dfrac{y}{xy+y+1}\le 1$$
becasuse After some simple computations, it is equivalent to
$$(1-xyz)^2\ge 0$$

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