Question

Rút gọn phân thức \(\dfrac{x^5+x^3+x^2+1}{x^3+x^2+x+1}\)

Answer 1

\(\dfrac{x^5+x^3+x^2+1}{x^3+x^2+x+1}=\dfrac{x^3\left(x^2+1\right)+\left(x^2+1\right)}{x^2\left(x+1\right)+\left(x+1\right)}\)

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

Answer 2

\(\dfrac{x^5+x^3+x^2+1}{x^3+x^2+x+1}=\dfrac{x^3.\left(x^2+1\right)+\left(x^2+1\right)}{x.\left(x^2+1\right)+\left(x^2+1\right)}\) \(=\dfrac{\left(x^3+1\right).\left(x^2+1\right)}{\left(x+1\right).\left(x^2+1\right)}=\dfrac{x^3+1}{x+1}=\dfrac{\left(x+1\right).\left(x^2-x+1\right)}{x+1}\)  \(=x^2-x+1\)

Answer 3

`(x^5+x^3+x^2+1)/(x^3+x^2+x+1)(x ne -1)`

`=(x^3(x^2+1)+x^2+1)/(x(x^2+1)+x^2+1)`

`=((x^2+1)(x^3+1))/((x^2+1)(x+1))`

`=(x^3+1)/(x+1)`

`=((x+1)(x^2-x+1))/(x+1)`

`=x^2-x+1`