计算：(a+2a2-2a-a-1a2-4a+4)÷4-aa2-2a．

题型：解答题难度：一般来源：山东

计算：(

a+2

a2-2a

-

a-1

a2-4a+4

)÷

4-a

a2-2a

．

答案

原式=[

a+2

a(a-2)

-

a-1

(a-2)2

]÷

4-a

a(a-2)

=[

a+2

a(a-2)

-

a-1

(a-2)2

]•

a(a-2)

4-a

=

a+2

4-a

-

a(a-1)

a-2

×

1

4-a

=

(a+2)(a-2)-a(a-1)

(4-a)(a-2)

=

a-4

(4-a)(a-2)

=-

a-4

(a-4)(a-2)

=-

1

a-2

．