(a-1)/(a+2)*(a²-4)/(a²-2a+1)÷1/(a²-1)
=(a-1)/(a+2)*(a-2)(a+2)/(a-1)^2÷1/(a²-1)
=(a-2)/(a-1)*(a+1)(a-1)
=(a-2)(a+1)
=a^2-a-2
=-2
(a-1)/(a+2)*(a²-4)/(a²-2a+1)÷1/(a²-1)
=(a-1)/(a+2)*(a-2)(a+2)/(a-1)^2÷1/(a²-1)
=(a-2)/(a-1)*(a+1)(a-1)
=(a-2)(a+1)
=a^2-a-2
=-2