We have to simplify : [1/(x-1)-1/(x+1)+1]*(x+1)/(x^2+1)

[1/(x-1)-1/(x+1)+1]*(x+1)/(x^2+1)

=> [((x+1) - (x - 1) + (x^2 - 1))/(x^2 -1)]*(x+1)/(x^2+1)

=> [(x + 1 - x + 1 + x^2 - 1)/(x^2 -1)]*(x+1)/(x^2+1)

=> [(x^2 + 1)/(x^2 -1)]*(x+1)/(x^2+1)

=> (x^2 + 1)*(x+1)/(x^2 -1)*(x^2+1)

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

=> (x+1)/(x - 1)(x + 1)

...

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We have to simplify : [1/(x-1)-1/(x+1)+1]*(x+1)/(x^2+1)

[1/(x-1)-1/(x+1)+1]*(x+1)/(x^2+1)

=> [((x+1) - (x - 1) + (x^2 - 1))/(x^2 -1)]*(x+1)/(x^2+1)

=> [(x + 1 - x + 1 + x^2 - 1)/(x^2 -1)]*(x+1)/(x^2+1)

=> [(x^2 + 1)/(x^2 -1)]*(x+1)/(x^2+1)

=> (x^2 + 1)*(x+1)/(x^2 -1)*(x^2+1)

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

=> (x+1)/(x - 1)(x + 1)

=> 1/(x - 1)

**The simplified form is 1/ (x - 1)**