f(x)=(x^2+1)/(x-2) Is it (x^2-5x+2)/(x-2)^2 ?
= (2x^2 - 4x - x^2 - 1/(x-2)^2 = (x^2 - 4x - 1)/(x-2)^2 so f ' (a) = (a^2 - 4a - 1)/(a-2)^2
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