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

题型：解答题难度：一般来源：不详

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

．