How to find the limit of this function as x approaches 1

1/(x-1) - 2/(x^2-1)

I've been stuck on this problem for days. Finding common denominator, factoring, cancelling, it isn't working. Help, please :'(

Common denominator:
[(x+1) - 2]/(x^2-1)=
(x-1)/(x^2-1)
lim x--->1 x-1/x^2-1=
x-1/(x+1)(x-1) =
1/(x+1) =
lim x--->1 1/(x+1) = 1/2
Bye

The LCD is(x+1)(x-1)

(x+1) - 2
--------------
(x+1)(x-1)

(x-1)
= -------------
(x+1)(x-1)

left with 1/(x+1) = 1/2