[tex]\dfrac{2x^3-2x^2-12x}{3x^2-6x}=\dfrac{2x\big(x^2-x-6\big)}{3x\big(x-2\big)}=
\dfrac{2\big(x^2-x-6\big)}{3\big(x-2\big)}=\\\\\\=\dfrac{2\big(x^2-3x+2x-6\big)}{3\big(x-2\big)}=\dfrac{2\Big[x\big(x-3\big)+2\big(x-3\big)\Big]}{3\big(x-2\big)}=
\dfrac{2\big(x-3\big)\big(x+2\big)}{3\big(x-2\big)}[/tex]
