SOLUTION: 2y/x^2+2x+1 + x/x^2-1

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We factor denominators first and get
2y/x^2+2x+1 + x/x^2-1 =
2y / (x+1)^2 + x / (x+1)(x-1)
The lowest common denominator is then
(x-1)(x+1)^2
We convert both fractions to that denominator and combine and get
2y / (x+1)^2 + x / (x+1)(x-1) =
2y(x-1) / (x-1)(x+1)^2 + x(x+1) / (x-1)(x+1)^2 =
[2y(x-1) + x(x+1)] / (x-1)(x+1)^2 =
No further significant simplification can be done...