The result of simplifying (a ^ 2 / A-1) - A-1 is

The result of simplifying (a ^ 2 / A-1) - A-1 is

=a²/(a-1)-(a+1)
=a²/(a-1)-(a+1)(a-1)/(a-1)
=[a²-(a+1)(a-1)]/(a-1)
=(a²-a²+1)/(a-1)
=1/(a-1)