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1a2+9+1b2+9+1c2+9\large \dfrac{1}{a^{2}+9} + \dfrac{1}{b^{2}+9} + \dfrac{1}{c^{2}+9} a2+91+b2+91+c2+91
Given that a,ba,ba,b and ccc are positive reals with a sum of 1. If the maximum value of the above expression can be expressed as xy\dfrac{x}{y}yx where xxx and yyy are coprime integers, find the value of x+yx+yx+y.
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