\(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)\(=\dfrac{2x^3-6x^2-x^2+3x-15x+45}{3x^3-9x^2-10x^2+30x+3x-9}\)\(=\dfrac{2x^2\left(x-3\right)-x\left(x-3\right)-15\left(x-3\right)}{3x^2\left(x-3\right)-10x\left(x-3\right)+3\left(x-3\right)}\)\(=\dfrac{\left(x-3\right)\left(2x^2-x-15\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\)\(=\dfrac{2x^2-x-15}{3x^2-10x+3}\)\(=\dfrac{2x^2-6x+5x-15}{3x^2-9x-x+3}\)\(=\dfrac{2x\left(x-3\right)+5\left(x-3\right)}{3x\left(x-3\right)-\left(x-3\right)}\)\(=\dfrac{\left(x-3\right)\left(2x+5\right)}{\left(x-3\right)\left(3x-1\right)}=\dfrac{2x+5}{3x-1}\)Câu trả lời: \(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)\(=\dfrac{2x^3-6x^2-x^2+3x-15x+45}{3x^3-9x^2-10x^2+30x+3x-9}\)\(=\dfrac{2x^2\left(x-3\right)-x\left(x-3\right)-15\left(x-3\right)}{3x^2\left(x-3\right)-10x\left(x-3\right)+3\left(x-3\right)}\)\(=\dfrac{\left(x-3\right)\left(2x^2-x-15\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\)\(=\dfrac{2x^2-x-15}{3x^2-10x+3}\)\(=\dfrac{2x^2-6x+5x-15}{3x^2-9x-x+3}\)\(=\dfrac{2x\left(x-3\right)+5\left(x-3\right)}{3x\left(x-3\right)-\left(x-3\right)}\)\(=\dfrac{\left(x-3\right)\left(2x+5\right)}{\left(x-3\right)\left(3x-1\right)}=\dfrac{2x+5}{3x-1}\)