(x+y^-1) (x^-1+y-1)
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=(x+(1÷y))((1÷x)+y-1)
=(x × (1÷x))+(x × y)+(x × -1)+((1÷y)×(1÷x))+((1÷y)×y)+((1÷y)×-1)
=1+xy+(-x)+(1÷xy)+1+(-1÷y)
=2+xy -x+(1÷xy)-(1÷y)
Hope it helps u.
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