Algebra problem.... me again

The problem is

2 + (1 / y + 1) - (1 / y - 1) = 0

Ok what I did was Mulitply the entire equation by the common denominator of

(y + 1)(y - 1).

I end up getting

2(y + 1)(y - 1) + y - 1 - y + 1 = 0

From here, I keep working the problem until it gets to

2(y^2 - 1) = 0

2y^2 - 2 = 0

(2y^2 - 2) / 2

y^2 - 1 = 0

y^2 = 1

Square root both sides to get

y = +- 1

The problem is, when entering either one of these solutions into the original problem, i'm always getting one of the divisions within the problem where the denominator is 0 and that is undefined....so i'm kinda lost. Is there no solution or?