Question

Rút gọn các phân thức sau:

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

b)\(\dfrac{x^3+3x^2-4}{x^3-3x+2}\)

Answer 1

a, \(\dfrac{x^4}{x^4+x^2}\)

b, \(\dfrac{x^3-x-4}{x^3+2}\)

Mk làm ra vậy á ko biết là có đúng hay sai nữa !!!

Answer 2

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

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

b: \(=\dfrac{x^3-x^2+4x^2-4}{x^3-x-2x+2}\)

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

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