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