先化简再求值（2X/X2-4 - 1/X+2）÷（X-1/X-2） X=√3-1
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解：
原式=[2x/(x²-4)-1/(x+2)]÷[(x-1)/(x-2)]
={2x/[(x+2)(x-2)]-(x-2)/[(x+2)(x-2)]}×[(x-2)/(x-1)]
=(2x-x+2)/[(x+2)(x-2)]×[(x-2)/(x-1)]
=(x+2)/[(x+2)(x-2)]×[(x-2)/(x-1)]
=1/(x-1)
=1/(√3-1-1)
=1/(√3-2)
=(√3+2)/[(√3+2)(√3-2)]
=(√3+2)/(√3²-2²)
=(√3+2)/(3-4)
= -√3-2
原式=[2x/(x²-4)-1/(x+2)]÷[(x-1)/(x-2)]
={2x/[(x+2)(x-2)]-(x-2)/[(x+2)(x-2)]}×[(x-2)/(x-1)]
=(2x-x+2)/[(x+2)(x-2)]×[(x-2)/(x-1)]
=(x+2)/[(x+2)(x-2)]×[(x-2)/(x-1)]
=1/(x-1)
=1/(√3-1-1)
=1/(√3-2)
=(√3+2)/[(√3+2)(√3-2)]
=(√3+2)/(√3²-2²)
=(√3+2)/(3-4)
= -√3-2
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