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x2(x+y)(x+z)+y2(y+x)(y+z)+z2(z+x)(z+y)<A{\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+x)(y+z)}+\frac{z^2}{(z+x)(z+y)}<A}(x+y)(x+z)x2+(y+x)(y+z)y2+(z+x)(z+y)z2<A
The above inequality is true for any positive numbers x,y,x, y,x,y, and zzz. Find the smallest number A,A,A, and prove that your answer is right.
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