Question

rút gọn phân thức

\(\dfrac{x^3+8x^2+19x+12}{x^3+6x^x+11x+6}\)

Answer 1

\(=\dfrac{x^3+x^2+7x^2+7x+12x+12}{x^3+x^2+5x^2+5x+6x+6}\)

\(=\dfrac{x^2\left(x+1\right)+7x\left(x+1\right)+12\left(x+1\right)}{x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x^2+7x+12\right)}{\left(x+1\right)\left(x^2+5x+6\right)}\)

\(=\dfrac{x^2+7x+12}{x^2+5x+6}\)

\(=\dfrac{x^2+3x+4x+12}{x^2+2x+3x+6}\)

\(=\dfrac{x\left(x+3\right)+4\left(x+3\right)}{x\left(x+2\right)+3\left(x+2\right)}\)

\(=\dfrac{\left(x+3\right)\left(x+4\right)}{\left(x+2\right)\left(x+3\right)}\)

\(=\dfrac{x+4}{x+2}\)