f(x) = (x^2 - 4) / (x - 3)^2
f'(x) = ((2·x)·(x - 3)^2 - (x^2 - 4)·2·(x - 3)) / (x - 3)^4
f'(x) = ((2·x)·(x - 3) - (x^2 - 4)·2) / (x - 3)^3
f'(x) = (2·x^2 - 6·x - 2·x^2 + 8) / (x - 3)^3
f'(x) = (8 - 6·x) / (x - 3)^3
f''(x) = (- 6·(x - 3)^3 - (8 - 6·x)·3·(x - 3)^2) / (x - 3)^6
f''(x) = (- 6·(x - 3) - (8 - 6·x)·3) / (x - 3)^4
f''(x) = (18 - 6·x + 18·x - 24) / (x - 3)^4
f''(x) = (12·x - 6) / (x - 3)^4