Answer
$$\frac{x+2}{2}$$
Work Step by Step
Using the rules of Algebra, we find:
$$\frac{x^2+5x+6}{2x+6} \\ \frac{\left(x+2\right)\left(x+3\right)}{2x+6} \\ \frac{\left(x+2\right)\left(x+3\right)}{2\left(x+3\right)} \\ \frac{x+2}{2}$$
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