Đáp án + Giải thích các bước giải:

 `1, 1/(x+1) - 1/(x^3 + 1) + 1/(x^2 - x + 1)`

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

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

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

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

`2, (x^2 + 2)/(x^3 - 1) + 2/(x^2 + x + 1) + 1/(1-x) (ĐK : x \ne 1)`

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

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

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

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

`3, (x^3 + 2x)/(x^3 + 1) + (2x)/(x^2 - x + 1) + 1/(x+1)`

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

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

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

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

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

`4, (3(x+1))^2/(x^3 - 1) - (1-x)/(x^2 + x + 1) + 3/(1-x) (ĐK : x \ne 1)`

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

`= (3x^2 + 6x + 3 + x^2 - 2x + 1 - 3x^2 - 3x - 3)/((x-1)(x^2 + x + 1))`

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

`= 1/(x-1)`