Question

1) Rút gọn các phân thức sau:

a) \(\dfrac{4x^3-8x^2+3x-6}{12x^3+4x^2+9x+3}\)

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

Answer 1

a,\(\dfrac{4x^3-8x^2+3x-6}{12x^3+4x^2+9x+3}=\dfrac{4x^2\left(x-2\right)+3\left(x-2\right)}{\text{ }\left(3x+1\right)4x^2+3\left(3x+1\right)}\)

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

Answer 2

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

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