To perform the indicated operations for the expression (2a+6)/(a^2+6a+9) + 1/(a+3), we first need to find a common denominator. The denominators of the two fractions are (a^2+6a+9) and (a+3). To get a common denominator, we can multiply the first fraction by (a+3)/(a+3), which gives:
(2a+6)/(a^2+6a+9) * (a+3)/(a+3) + 1/(a+3)
= (2a+6)(a+3)/(a+3)(a^2+6a+9) + (a^2+6a+9)/(a+3)(a^2+6a+9)
= (2a^2+12a+18+a^2+6a+9)/(a^2+6a+9)(a+3)
= (3a^2+18a+27)/(a+3)(a^2+6a+9)
= 3(a+3)(a+3)/(a+3)(a+3)(a+1)
= 3/(a+1)
Therefore, the simplified form of the expression is 3/(a+1).