Question

Rút gọn phân thức 8x^3+y^3/y^3+2xy^2+y^2-4x^2

 

Answer 1

\(\dfrac{8x^3+y^3}{y^3+2xy^2+y^2-4x^2}\\ =\dfrac{\left(2x+y\right)\left(4x^2-2xy+y^2\right)}{\left(y^3+2xy^2\right)+\left(y^2-4x^2\right)}\\ =\dfrac{\left(2x+y\right)\left(4x^2-2xy+y^2\right)}{y^2\left(y+2x\right)+\left(y-2x\right)\left(y+2x\right)}\\ =\dfrac{\left(y+2x\right)\left(4x^2-2xy+y^2\right)}{\left(y+2x\right)\left(y^2+y-2x\right)}\\ =\dfrac{4x^2-2xy+y^2}{y^2+y-2x}\)

Answer 2

\(\dfrac{8x^3+y^3}{y^3+2xy^2+y^2-4x^2}\)

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

\(=\dfrac{4x^2-2xy+y^2}{y^2+y-2x}\)