100 Followers problem!

Algebra Level 4

There are 2011 positive numbers with both their sum and the sum of their reciprocals equal to 2012. Let \(x\) be one of these numbers, if the maximum value of \(x +\dfrac{1}{x} \) can be expressed as \( \frac ab\) for coprime positive integers, submit your answer as \(a-b\).

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