Đáp án+Giải thích các bước giải:

 `(3x+1)/((x-1)^{2})-(1)/(x+1)+(x+3)/(1-x^{2})`

`(x\ne\pm1)`

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

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

`=(2x^{2}+2x+4-x^{2}+2x-1)/((x-1)^{2}.(x+1))`

`=(x^{2}+4x+3)/((x-1)^{2}.(x+1))`

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

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

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