先化简,再求值(a的平方-4a+4分之a的平方-4-2-a分之1)除以a平方-2a分之2,其中a是方程x的平方+3x+1=0的根

[(a²-4)/(a²-4a+4)-1/(2-a)]÷2/(a²-2a)
=[(a-2)(a+2)/(a-2)²+1/(a-2)]×a(a-2)/2
=[(a+2)/(a-2)+1/(a-2)]×a(a-2)/2
=(a+3)/(a-2)×a(a-2)/2
=a(a+3)/2
=(a²+3a)/2
将x=a代入方程中,得：a²+3a+1=0,所以a²+3a=-1
所以原式=(-1)/2=-1/2