Find f'(a).

f(x)=(x^2+1)/(x-2)

Is it (x^2-5x+2)/(x-2)^2 ?

f ' (x) = ( (x-2)(2x) - (x^2 + 1)(1) )/(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