Limit with a Zing

Calculus Level 2

Let \(a\) be a positive integer such that the following limit exists: \[\lim_{x\to 1} \left( \frac{1}{x-1} - \frac{1}{x^a-2x+1}\right).\] If the value of the limit is \(b,\) find \(a+b.\)

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