Question

[Đỗ Tiến Dũng]

mn giúp mik với mik cảm ơn

quy đồng rồi rút gọn phân thức sau 

x³+2x/x³+1 +2x/x²-x+1 + 1/x+1

Answer 1

[Dang Tung]

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

Answer 2

[Trịnh Minh Hoàng]

Ta có:
`\frac{x^3 + 2x}{x^3 + 1} + \frac{2x}{x^2 - x + 1} + \frac{1}{x + 1}`
Mẫu số chung là: `M = (x + 1)(x^2 - x + 1)`
`= \frac{x^3 + 2x}{(x + 1)(x^2 - x + 1)} + \frac{2x(x + 1)}{(x + 1)(x^2 - x + 1)} + \frac{x^2 - x + 1}{(x + 1)(x^2 - x + 1)}`
`= \frac{x^3 + 2x + 2x(x + 1) + x^2 - x + 1}{(x + 1)(x^2 - x + 1)}`
`=\frac{x^3 + 3x^2 + 3x + 1}{(x + 1)(x^2 - x + 1)}`
Vậy: Phân thức quy đồng, rút gọn là: `\frac{x^3 + 3x^2 + 3x + 1}{(x + 1)(x^2 - x + 1)}`