Since a^2-b^2 can also be written as (a+b)(a-b), we can do that with a^2 and 1^2 to get (a+1)(a-1). For the denominator, a is clearly in both, so we factor that out to get a*(a-1), resulting in ((a+1)(a-1))/((a)(a-1)). Crossing out the a-1, we get a+1/a