Which inequality should I apply?

Algebra Level 3

x2x+y+z+yx+2y+z+zx+y+2z \large\frac x{2x+y+z} + \frac y{x+2y+z} + \frac z{x+y+2z}

Let x,yx,y and zz be positive numbers. Find the maximum value of the expression above.

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