To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]