Multiply out the denominator (the (x+1)(x-1) ) and then simplify the denominator.
After doing that, you'll be able simplify greatly by looking to simplify between the numerator and denominator.
Are you practicing for class or perhaps you're studying on your own? I'm just asking this so that there might be an "official" name to this class of polynomial. If you do know, google the title and add "worksheets", and there should be many sources.
From what I'm seeing, these problems are leading to (or from) factorization, difference of squares, binomial reduction and polynomial reduction.