$\text{Tử số:}$
$\text{2x³-7x²-12x + 45}$
$\text{=2x³-6x²-x²+3x-15x+45}$
$\text{=2x²(x-3)-x(x-3)-15(x-3)}$
$\text{=(x-3)(2x²-x-15)}$
$\text{=(x-3)(2x²-6x+5x-15)}$
$\text{=(x-3)[2x(x-3)+5(x-3)]}$
$\text{=(x-3)(x-3)(2x+5)}$
$\text{=(x-3)²(2x+5)}$
$\text{Mẫu số:}$
$\text{3x³-19x²+33x-9}$
$\text{=3x³-9x²-10x²+30x+3x-9}$
$\text{=3x²(x-3)-10x(x-3)+3(x-3)}$
$\text{=(x-3)(3x²-10x+3)}$
$\text{=(x-3)(3x²-9x-x+3)}$
$\text{=(x-3)[3x(x-3)-(x-3)]}$
$\text{=(x-3)(x-3)(3x-1)}$
$\text{=(x-3)²(3x-1)}$
$\frac{2x³-7x²-12x + 45}{3x³-19x²+33x-9}$
=$\frac{(x-3)²(2x+5)}{(x-3)²(3x-1)}$
=$\frac{2x+5}{3x-1}$
