Finding the derivative using quotient rule... $$\frac{\text{d}}{\text{dt}}\dfrac{2(t+2)^2}{(t-2)^2}$$
I applied the quotient rule:
$$\dfrac{[2(t+2)^2]'(t-2)^2-2(t+2)^2[(t-2)^2]'}{(t-2)^4}$$
$$\dfrac{4(t+2)(t-2)^2-2(t+2)^22(t-2)}{(t-2)^4}$$
$$\dfrac{4(t+2)(t-2)-4(t+2)^2}{(t-2)^3}$$
This was part of a problem where I needed to find the second derivative of a parametric curve but I am stuck on finding this derivative. I typed this problem into wolfram alpha and it gave me $\dfrac{-(16 (x+2))}{(x-2)^3}$, I've been working on this problem for the past hour and can't figure out what I am doing wrong, could someone please explain how to do this?

Note that $4(t+2)(t-2)-4(t+2)^2=-16(t+2).$ Hence, you are correct.
