a/(a+2)-1 = -(3a+2)/(a^2+4a+4)

a/(a+2)-1 = -(3a+2)/(a^2+4a+4)

a/(a+2)-1 = -(3a+2)/((a+2)(a+2))
multiply each term by (a+2)(a+2)

a(a+2) - (a+2)(a+2) = -3a-2
a^1 + 2a - a^2 - 4a - 4 = -3a-2
a = 2