# A geometric inequality?

Algebra Level 4

${\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+x)(y+z)}+\frac{z^2}{(z+x)(z+y)}<A}$

The above inequality is true for any positive numbers $$x, y,$$ and $$z$$. Find the smallest number $$A,$$ and prove that your answer is right.

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