{a^2-4/(a^2-4a+4)-2/a-2}÷a^2+2a/a-2
=[(a+2)(a-2)/(a-2)² -2/(a-2)]×(a-2)/a(a+2)
=[(a+2)/(a-2)-2/(a-2)]×(a-2)/a(a+2)
=a/(a-2)×(a-2)/a(a+2)
=1/(a+2)
取a=-1
原式=1/(-1+2)=1
{a^2-4/(a^2-4a+4)-2/a-2}÷a^2+2a/a-2
=[(a+2)(a-2)/(a-2)² -2/(a-2)]×(a-2)/a(a+2)
=[(a+2)/(a-2)-2/(a-2)]×(a-2)/a(a+2)
=a/(a-2)×(a-2)/a(a+2)
=1/(a+2)
取a=-1
原式=1/(-1+2)=1