化简求值:[3/x-1-(x-1)]除以x^2-4x+4/x-1,其中x=-1
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解
[3/(x-1)-(x-1)]÷(x²-4x+4)/(x-1)
=[3/(x-1)-(x-1)]×(x-1)/(x-2)²
=3/(x-2)²-(x-1)²/(x-2)²
=[3-(x-1)²]/(x-2)²
=(3-x²+2x-1)/(x-2)²
=(-x²+2x+2)/(x-2)²
=(-1-2+2)/(-3)²
=-1/9
[3/(x-1)-(x-1)]÷(x²-4x+4)/(x-1)
=[3/(x-1)-(x-1)]×(x-1)/(x-2)²
=3/(x-2)²-(x-1)²/(x-2)²
=[3-(x-1)²]/(x-2)²
=(3-x²+2x-1)/(x-2)²
=(-x²+2x+2)/(x-2)²
=(-1-2+2)/(-3)²
=-1/9
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