[3x/(x+1)-x/(x-1)]/[(x-2)/(x^-1)],其中x=2分之根号2

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[3x/(x+1)-x/(x-1)]/[(x-2)/(x^-1)],其中x=2分之根号2
[3x/(x+1)-x/(x-1)]/[(x-2)/(x^-1)],其中x=2分之根号2

[3x/(x+1)-x/(x-1)]/[(x-2)/(x^-1)],其中x=2分之根号2
先化简后求值：[3x/(x+1)-x/(x-1)]/[(x-2)/(x²-1)],其中x=(√2)/2
原式={[3x(x-1)-x(x+1)]/(x²-1)}×[(x²-1)/(x-2)]={[2x(x-2)]/(x²-1)}×[(x²-1)/(x-2)]=2x=√2.

分子分母同乘x^-1得：
原式=[3/(x+1)-1/(x-1)]/(x-2)
=[2(x-2)/(x²-1)]/(x-2)
=2/(x²-1)
=-4

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