5. cimplify \( \frac{x^{2}+5 x+6}{x+2} \)

To simplify \( \frac{x^{2}+5x+6}{x+2} \), we first factor the numerator. The expression \( x^2 + 5x + 6 \) can be factored into \( (x + 2)(x + 3) \). Now, we have: \[ \frac{(x + 2)(x + 3)}{x + 2} \] As long as \( x \neq -2 \), we can cancel \( x + 2 \) from the numerator and the denominator: \[ x + 3 \] So the simplified expression is \( x + 3 \), for \( x \neq -2 \).