you want to factor the quadratic to get:
x^2 + 5x + 6 is equal to (x + 3) * (x + 2)
your expression becomes:
(x + 3)
-------------------
(x + 3) * (x + 2)
the (x + 3) in the numerator and denominator cancel out and you are left with:
1
-----------------
(x + 2)