问题 解答题
先化简,再求值:(
x+2
x2-2x
-
x-1
x2-4x+4
)÷
x-4
x3-2x2
,x=-2.
答案

原式=(

x+2
x(x-2)
-
x-1
(x-2)2
)÷
x-4
x2(x-2)

=

(x+2)(x-2)-x(x-1)
x(x-2)2
×
x2(x-2)
x-4

=

x2-4-x2+x
x(x-2)2
×
x2(x-2)
x-4

=

x-4
x(x-2)2
×
x2(x-2)
x-4

=

x
x-2

当x=-2时,原式=

-2
-2-1
=
2
3

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