Question

Rút gọn phân thức

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

Answer 1

\(\dfrac{\left(x-2\right)^2\left(2x+2x^2\right)}{\left(x+1\right)\left(4x-x^3\right)}\\ =\dfrac{\left(x-2\right)^22x\left(1+x\right)}{\left(x+1\right)x\left(4-x^2\right)}\\ =\dfrac{2\left(x-2\right)^2}{\left(2-x\right)\left(2+x\right)}\\ =\dfrac{2\left(2-x\right)^2}{\left(2-x\right)\left(2+x\right)}\\ =\dfrac{2\left(2-x\right)}{2+x}\)