Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \(\frac{{{x^{\rm{m}}}{y^{\rm{n}}}}}{{\left( {1 + {x^{2{\rm{m}}}}} \right)\left( {1 + {y^{2{\rm{n}}}}} \right)}}\) is:

Let x, y be positive real numbers and m, n positive integers. The maxi

1.	Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \(\frac{{{x^{\rm{m}}}{y^{\rm{n}}}}}{{\left( {1 + {x^{2{\rm{m}}}}} \right)\left( {1 + {y^{2{\rm{n}}}}} \right)}}\) is:
A.	1
B.	\(\frac{1}{2}\)
C.	\(\frac{1}{4}\)
D.	\(\frac{{m + n}}{{6\:mn}}\)
Answer» D. \(\frac{{m + n}}{{6\:mn}}\)

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Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \(\frac{{{x^{\rm{m}}}{y^{\rm{n}}}}}{{\left( {1 + {x^{2{\rm{m}}}}} \right)\left( {1 + {y^{2{\rm{n}}}}} \right)}}\) is:

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