Calc
posted by CMM on .
Find f'(a).
f(x)= (x^2 + 1)/(x  2)
So,
[[(a + h)^2 + 1]/[(a + h)  2]]  [(a^2 + 1)/a  2] and the whole thing divided by h
I tried simplifying it and ended up with [a + h/2]  (a2), which is incorrect. I used wolfram alpha and got (a^2  4a  1)/(a  2)^2 but I do not know how to get this. Please help.

numerator
(a^2+2ah+h^2+1)(a2) (a^2+1)(a+h2)
a^3+2a^2h+ah^2+a2a^24ah2h^22 a^3aa^2hh+2a^2+2
that is
a^2h + ah^2 4ah h
divide numerator by h
a^2 +ah 4a 1
let h>0
a^24a1 sure enough now denominator
(a2)(a+h2)
let h>0
(a2)^2 sure enough