先化简再求值:(1-1/x)/(x^2-2x+1)/(x^2-1),其中x=根号2
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(1-1/x)/(x^2-2x+1)/(x^2-1)
=[(x-1)/x]/[(x+1)(x+1)]/[(x+1)(x-1)]
=[(x-1)/x]/[(x+1)/(x-1)]
=1/x/[(x+1)
=1/[x(x+1)]
=1/(2+根号2)
=(2-根号2)/[(2+根号2)(2-根号2)]
=(2-根号2)/2
=[(x-1)/x]/[(x+1)(x+1)]/[(x+1)(x-1)]
=[(x-1)/x]/[(x+1)/(x-1)]
=1/x/[(x+1)
=1/[x(x+1)]
=1/(2+根号2)
=(2-根号2)/[(2+根号2)(2-根号2)]
=(2-根号2)/2
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