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Let aaa be a positive integer such that the following limit exists: limx→1(1x−1−1xa−2x+1).\lim_{x\to 1} \left( \frac{1}{x-1} - \frac{1}{x^a-2x+1}\right).x→1lim(x−11−xa−2x+11). If the value of the limit is b,b,b, find a+b.a+b.a+b.
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