Your factorized version makes clear that all the terms

x^2 + 5x + 6

are all in the numerator. But you still haven't clarified whether that +1 at the end is in the denominator.

You should add grouping indicators to clarify this. If the problem is

(x^2 + 5x + 6) / (2x + 1)

then I agree; the only thing we can do is factor the numerator to get

(x+3) (x+2) / (2x+1)

On the other hand, if the problem is actually

[(x^2 + 5x + 6) / (2x)] + 1

then we can perhaps do more:

[(x^2 + 5x + 6) / (2x)] + [(2x)/(2x)]

= (x^2 + 7x + 6) / (2x)

= (x+6) (x+1) / (2x)