$\frac{x+2}{x^{2}+5 x+6}$

Step 1 ：Given the rational function \(\frac{x+2}{x^{2}+5 x+6}\).

Step 2 ：To simplify it, we can factor the denominator and then cancel out any common factors with the numerator.

Step 3 ：The denominator factors as \((x+2)(x+3)\).

Step 4 ：Cancelling out the common factor of \(x+2\) in the numerator and denominator, we get \(\frac{1}{x+3}\).

Step 5 ：Final Answer: \(\boxed{\frac{1}{x+3}}\)