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