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现化简,在求值,x-2分之3-x除以（x+2-x-2分之5）,其中x=4.

分类: 作业答案 • 2021-12-19 17:27:37
问题描述：

现化简,在求值,x-2分之3-x除以（x+2-x-2分之5）,其中x=4.

答

(3-x)/(x-2)÷[x+2-5/(x-2)]
=(3-x)/(x-2)÷[(x+2)(x-2)-5]/(x-2)
=(3-x)/(x-2)÷[(x^2-9)/(x-2)]
=-(x-3)/(x-2)×[(x-2)/(x-3)(x+3)]
=-1/(x+3)
=-1/(4+3)
=-1/7

答

(3-x)/(x-2)÷[x+2-5/(x-2)]
=(3-x)/(x-2)÷[(x+2)(x-2)/(x-2)-5/(x-2)]
=(3-x)/(x-2)÷[(x^2-4)/(x-2)-5/(x-2)]
=(3-x)/(x-2)÷[(x^2-4-5)/(x-2)]
=(3-x)/(x-2)÷[(x^2-9)/(x-2)]
=(3-x)/(x-2)*(x-2)/(x^2-9)
=(3-x)/(x^2-9)
=-(x-3)/(x^2-9)
=-(x-3)/(x-3)(x+3)
=-1/(x+3)
=-1/(4+3)
=-1/7

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