Question

化简求值(3x/x+2-x/x-2)÷x/x的平方-4,其中x=-3

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Answer 1

解：
原式=[3x/(x+2)-x/(x-2)]÷[x/(x²-4)]
={3x(x-2)/[(x+2)(x-2)]-x(x+2)/[(x+2)(x-2)]}÷{x/[(x+2)(x-2)]}
={[3x-x(x+2)]/[(x+2)(x-2)]}×[(x+2)(x-2)/x]
={-x²+x)/[(x+2)(x-2)]}×[(x+2)(x-2)/x]
={-x(x-1)/[(x+2)(x-2)]}×[(x+2)(x-2)/x]
=1-x
=1-(-3)
=1+3
=4