Add the expressions. Combine like terms if possible. \( \frac{5 x}{(x+3)^{2}}+\frac{1}{x+3} \) The numerator of your answer is : The denominator of your answer is :

To add the expressions \( \frac{5 x}{(x+3)^{2}} \) and \( \frac{1}{x+3} \), we first need a common denominator. The common denominator is \( (x+3)^{2} \). Now, we rewrite the second fraction with the common denominator: \[ \frac{1}{x+3} = \frac{1 \cdot (x+3)}{(x+3) \cdot (x+3)} = \frac{x+3}{(x+3)^{2}} \] Now we can add the fractions: \[ \frac{5 x}{(x+3)^{2}} + \frac{x+3}{(x+3)^{2}} = \frac{5 x + (x + 3)}{(x+3)^{2}} = \frac{5 x + x + 3}{(x+3)^{2}} = \frac{6 x + 3}{(x+3)^{2}} \] Now, we can combine like terms in the numerator: 1. The numerator of your answer is: \( 6x + 3 \) 2. The denominator of your answer is: \( (x+3)^{2} \)