[（a^2-5a+2)/(a+2)+1]÷(a^2-4)/(a^2+4a+4)
=(a^2-4a+4)/(a+2)÷(a-2)(a+2)/(a+2)^2
=(a-2)^2/(a+2)÷(a-2)/(a+2)
=a-2