化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]

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化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
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化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]

化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]

解
原式
=[(x+2)/(x-2)(x+2)-(2x-5)/(x-2)²]×(x-2)/(x-3)
=[1/(x-2)-(2x-5)/(x-2)²]×(x-2)/(x-3)
=1/(x-3)-(2x-5)/(x-2)(x-3)
=(x-2)/(x-2)(x-3)-(2x-5)/(x-2)(x-3)
=(x-2-2x+5)/(x-2)(x-3)
=(-x+3)/(x-2)(x-3)
=-1/(x-2)

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