Question

Rút gọn phân thức

1). \(\dfrac{x^4-y^4}{y^3-x^3}\)

2). \(\dfrac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}\)

3). \(\dfrac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}\)

Answer 1

1) \(\dfrac{x^{4^{ }}-y^4}{y^3-x^3}=\dfrac{\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)}{-\left(x-y\right)\left(x^2+xy+y^2\right)}\)

\(=\dfrac{x^3+x^2y+xy^2+y^3}{-x^2-xy-y^2}\)

2) \(\dfrac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}=\dfrac{2x^2-6x-4x+12}{\left(x-2\right)\left(3x^2-27\right)}\\ =\dfrac{2x\left(x-2\right)-6\left(x-2\right)}{\left(x-2\right)\left(3x^2-27\right)}\\ =\dfrac{2x-6}{3x^2-27}\\ =\dfrac{2\left(x-3\right)}{3\left(x-3\right)\left(x+3\right)}\\ =\dfrac{2}{3x+9}\)

3)

\(\dfrac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}=\dfrac{2x\left(x^2-1\right)+\left(x^2-1\right)}{x\left(x^2-1\right)+2\left(x^2-1\right)}\\ =\dfrac{2x+1}{x+2}\)