(2a+2)/(a-1)/(a+1)-(a^2-1)/(a^2-2a+1)
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(2a+2)/(a-1)/(a+1)-(a^2-1)/(a^2-2a+1)
=2(a+1)/[(a-1)(a+1)]-(a-1)(a+1)/(a-1)^2
=2/(a-1)-(a+1)/(a-1)
=[2-(a+1)]/(a-1)
=[2-a-1]/(a-1)
=(1-a)/(a-1)
=-(a-1)/(a-1)
=-1
=2(a+1)/[(a-1)(a+1)]-(a-1)(a+1)/(a-1)^2
=2/(a-1)-(a+1)/(a-1)
=[2-(a+1)]/(a-1)
=[2-a-1]/(a-1)
=(1-a)/(a-1)
=-(a-1)/(a-1)
=-1
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