Đáp án+Giải thích các bước giải:

`b,\frac{x^3+2x}{x^3+1}+\frac{2x}{x^2-x+1}+\frac{1}{x+1}`         (ĐK:`x \ne -1`)

`=\frac{x^3+2x}{(x+1)(x^2-x+1)}+\frac{2x}{x^2-x+1}+\frac{1}{x+1}`  

`=\frac{x^3+2x+2x(x+1)+x^2-x+1}{(x+1)(x^2-x+1)}`

`=\frac{x^3+2x+2x^2+2x+x^2-x+1}{(x+1)(x^2-x+1)}`

`=\frac{x^3+3x^2+3x+1}{(x+1)(x^2-x+1)}`

`=\frac{x^3+x^2+2x^2+2x+x+1}{(x+1)(x^2-x+1)}`

`=\frac{x^2(x+1)+2x(x+1)+(x+1)}{(x+1)(x^2-x+1)}`

`=\frac{(x+1)(x^2+2x+1)}{(x+1)(x^2-x+1)}`

`=\frac{x^2+2x+1}{x^2-x+1}`

`=\frac{(x+1)^2}{x^2-x+1}`

 `c,\frac{1}{x}+\frac{1}{x+5}+\frac{x-5}{x^2+5x}`                  (ĐK:`x \ne 0,x \ne -5`)

`=\frac{1}{x}+\frac{1}{x+5}+\frac{x-5}{x(x+5)}`

`=\frac{x+5+x+x-5}{x(x+5)}`

`=\frac{3x}{x(x+5)}`

`=\frac{3}{x+5}`

`b) (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)`

`c) 1/x + 1/(x+5) + (x-5)/(x^2 + 5x)`

`= 1/x + 1/(x+5) + (x-5)/(x(x+5))`

`= (x+5)/(x(x+5)) + x/(x(x+5)) + (x-5)/(x(x+5))`

`= ( x + 5 + x + x - 5 )/(x(x+5))`

`= (3x)/(x(x+5))`

`= 3/(x+5)`