(2 / (x+1)/(x-1) – (2/2)/(x-1)

= 2/[(x+1)(x-1)] – 2/[2(x-1)]

finding a common denominator would require multiplying the first term by 2/2 and the second term by (x+1)/(x+1) so this becomes

4/[2(x+1)(x-1)] – 2(x+1)/[2(x+1)(x-1)]

the two numerators now over the common denominator gives you:

[4-2(x+1)]/[2(x+1)(x-1)]

expanding the numerator you get

(4-2x-2)/[2(x+1)(x-1)]

=(2-2x)/[2(x+1)(x-1)]

=2(1-x)/[2(x+1)(x-1)]

Now, this is tricky, because you want to simplify this. In the numerator you have 1-x, but you want either x+1 or x-1 like there is in the denomintor. If you pull a negative out of the 1-x and put it in front of the two instead, you get

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

Now you have a 2 in the numerator and denominator and an x-1 in both as well. You can factor them out to get

-1/(x+1).

This isn’t exactly the answer you had, but it is correct given the equation you gave.