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If xxx and yyy are positive real numbers and m,nm,nm,n are positive integers, then what is the maximum value of xm⋅yn(1+x2m)⋅(1+y2n)\dfrac{x^m \cdot y^n}{(1+x^{2m}) \cdot (1+y^{2n})}(1+x2m)⋅(1+y2n)xm⋅yn
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