化简[（x²-1）/（x²-2x+1)+(1-x)/(x+1)]÷[x/(x-1)]
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原式=[(x+1)(x-1)/(x-1)²-(x-1)/(x+1)]*(x-1)/x
=[(x+1)/(x-1)-(x-1)/(x+1)]*(x-1)/x
=(x²+2x+1-x²+2x-1)/(x+1)(x-1)*(x-1)/x
=2x/(x+1)(x-1)*(x-1)/x
=2/(x+1)
=[(x+1)/(x-1)-(x-1)/(x+1)]*(x-1)/x
=(x²+2x+1-x²+2x-1)/(x+1)(x-1)*(x-1)/x
=2x/(x+1)(x-1)*(x-1)/x
=2/(x+1)
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