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

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

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

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

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

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

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

**The required result is (x - y + 1)/ (x + y + 1)**