199 upvotes problem

Algebra Level 4

1a2+9+1b2+9+1c2+9\large \dfrac{1}{a^{2}+9} + \dfrac{1}{b^{2}+9} + \dfrac{1}{c^{2}+9}

Given that a,ba,b and cc are positive reals with a sum of 1. If the maximum value of the above expression can be expressed as xy\dfrac{x}{y} where xx and yy are coprime integers, find the value of x+yx+y.

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