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

原式=[

x+2
x(x-2)
-
x-1
(x-2)2
]+
x-4
x

=[

x2-4
x(x-2)2
-
x2-x
x(x-2)2
]+
x-4
x

=

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

=

x-4
x(x-2)2
+
x-4
x

=

(x-4)(x-2)2
x(x-2)2

=

x3+20x-16
x(x-2)2

当x=-1时,原式=

-1-20-16
-1×(-1-2)2
=
37
9

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