# Maxima of Sum of Reciprocals!

$\large{\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} < 1}$

If $$a,b,c$$ are three positive integers satisfying the above inequality, then let $$S$$ be the maximum possible value of $$\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}$$. If $$S$$ can be expressed as $$\dfrac{P}{Q}$$ for positive coprime integers $$P,Q$$ then find the value of $$P+Q$$.

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