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[ (x-1+x+1)/(x-1) ] / [ (x+1-x+1)/(x²-1) ]
( 2x / x-1 ) / ( 2 / x²-1 )
(2x)(x²-1) / 2(x-1)
x(x+1)(x-1) / (x-1)
= x(x+1)