Does f(x)=(2x^3-2x)/x^3+x^2-4x-4 have any horizontal asymptotes? How can you tell?
f(x) increases without limit where the denominator is zero, but those would be vertical asymptotes.
Is your denominator x^3 or (x^3+x^2-4x-4) ? If the latter, you should use parentheses around it.
By using factoring and polynomial long division, you will find that
(2x^3-2x)/(x^3+x^2-4x-4)
= 2(x+1)(x-1)/[(x-2)(x+2)(x+1)]
= 2(x-1)/[(x-2)(x+2)]
The function is zero at x=1, but that is not a horizontal asymptote. There is no range of x values for whih the function approaches a constant (y) value asymptotically.