Đáp án+Giải thích các bước giải:

 `(x+1)/(x-2)+(2x)/(x+2)+(5x+2)(4-x^2)` (Điều kiện xác định: `x \ne +-2`)

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

`=(x+1)/(x-2)+(2x)/(x+2)+(5x+2)/[(2-x)(2+x)]`

`=[(x+1)(x+2)]/[(x+2)(x-2)]+[2x(x-2)]/[(x+2)(x-2)]-(5x+2)/[(x+2)(x-2)]`

`=[x(x+2)+(x+2)]/[(x+2)(x-2)]+(2x^2-4x)/[(x+2)(x-2)]-(5x+2)/[(x+2)(x-2)]`

`=(x^2+2x+x+2)/[(x+2)(x-2)]+(2x^2-4x)/[(x+2)(x-2)]-(5x+2)/[(x+2)(x-2)]`

`=(x^2+3x+2)/[(x+2)(x-2)]+(2x^2-4x)/[(x+2)(x-2)]-(5x+2)/[(x+2)(x-2)]`

`=(x^2+3x+2+2x^2-4x-5x-2)/[(x+2)(x-2)]`

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

`=[3x(x-2)]/[(x+2)(x-2)]`

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

`(x+1)/(x-2) + (2x)/(x+2) + (5x+2)/(4-x^2)` (ĐK: `x \ne 2; -2)`

`= (x+1)/(x-2) + (2x)/(x+2) + (5x+2)/((2 - x)(x+2))`

`= (x+1)/(x-2) + (2x)/(x+2) - (5x+2)/((x-2)(x+2))`

`= ((x+1)(x+2))/((x-2)(x+2)) + ((2x)(x-2))/((x-2)(x+2)) - (5x+2)/((x-2)(x+2))`

`= (x^2 + 3x + 2)/((x-2)(x+2)) + (2x^2 - 4x)/((x-2)(x+2)) - (5x+2)/((x-2)(x+2))`

`= (x^2 + 3x + 2 + 2x^2 - 4x - 5x-2)/((x-2)(x+2))`

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

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

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