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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)(a-1)
=1/(a-1)(a+1)
[b/(a²-ab)+a/(b²-ab)]÷(a-b)/ab
=[b/a(a-b)+a/b(b-a)]÷(a-b)/ab
=[b²/ab(a-b)-a²/ab(a-b)]÷(a-b)/ab
=(b²-a²)/ab(a-b)*ab/(a-b)
=(a+b)(b-a)/ab(a-b)*ab/(a-b)
=-(a+b)/(a-b)
=a²/(a-1)-(a+1)(a-1)/(a-1)
=[a²-(a-1)(a+1)]/(a-1)
=(a²-a²+1)/(a+1)(a-1)
=1/(a-1)(a+1)
[b/(a²-ab)+a/(b²-ab)]÷(a-b)/ab
=[b/a(a-b)+a/b(b-a)]÷(a-b)/ab
=[b²/ab(a-b)-a²/ab(a-b)]÷(a-b)/ab
=(b²-a²)/ab(a-b)*ab/(a-b)
=(a+b)(b-a)/ab(a-b)*ab/(a-b)
=-(a+b)/(a-b)
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