`a) (3x+1)/((x-1)^2) - 1/(x+1) + (x+3)/(1-x^2) (x \ne +- 1)`

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

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

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

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

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

`b) (2x)/(x^2-4) - (2/(x+5) + (3-x)/(x+1)) + [2/(x+5) - (4/(x^2-4) + (x-3)/(x+1))] (x \ne +- 2; x \ne -5; x \ne -1)`

`=(2x)/(x^2-4) - 2/(x+5) - (3-x)/(x+1) + 2/(x+5) - 4/(x^2-4) - (x-3)/(x+1)`

`=((2x)/((x-2)(x+2)) - 4/((x-2)(x+2))) + ((-2)/(x+5) + 2/(x+5)) + ((x-3)/(x+1) - (x-3)/(x+1))`

`=(2(x-2))/((x-2)(x+2)) + 0 + 0`

`=2/(x+2)`