Factoring will make things much easier here. The first fraction will look like
(x+1)^2
------------- and the second, after inversion, will look like 1 / [ 2x (x+1) ].
(x-1)(x+1)
Then all you have to do is to simplify:
(x+1)^2 1
------------- * ---------------
(x-1)(x+1) (2x)(x+1)
After your first cancelling, you'll have:
(x+1) 1
------------- * ---------------
(x-1)(x+1) (2x)
and after your second, you'll have:
1 1 1
------------- * --------- = ------------- (answer)
(x-1) (2x) (2x)(x-1)