（a-2/a²-2a - a-1/a²+4a+4）÷ a-4/a+2

题目

（a-2/a²-2a - a-1/a²+4a+4）÷ a-4/a+2
其中a满足a²+2a+1=0

答案

a²+2a-1=0
a²+2a=1
原式=[(a-2)/a(a+2)-(a-1)/(a+2)²]×(a+2)/(a-4)
={[(a-2)(a+2)-a(a-1)]/a(a+2)²}×(a+2)/(a-4)
=(a²-4-a²+a)(a+2)/[a(a-4)(a+2)²]
=(a-24)(a+2)/[a(a-4)(a+2)²]
=1/(a²+2a)
=1/1
=1