(k) \( \frac{x^{2}+5 x+6}{(x+3)^{2}} \)

To simplify \( \frac{x^{2}+5 x+6}{(x+3)^{2}} \), we start by factoring the numerator. The expression \( x^{2}+5x+6 \) factors to \( (x+2)(x+3) \). This means we can rewrite the original expression as: \[ \frac{(x+2)(x+3)}{(x+3)^{2}} \] Next, we see that we can cancel out one \( (x+3) \) from the numerator and the denominator, since \( x+3 \neq 0 \). This gives us a simplified expression: \[ \frac{x+2}{x+3} \] So, the simplified form of the original expression is: \[ \frac{x+2}{x+3} \] Now the function is easier to work with, revealing its behavior and making it simpler for calculus or further algebraic manipulation.