Evaluate undersetx→2lim(x^6-24x-16)/(x^3+2x-12).

$\underset{x→2}{\lim}\frac{x^6-24x-16}{x^3+2x-12}=\underset{x→2}{\lim}\frac{(x-2)(x^5+2x^4+4x^3+8x^2+16x+8)}{(x-2)(x^2+2x+6)}=\frac{168}{14}=12$