\begin{align*} \text{Write as a single fraction:} \\ \\ \frac{1}{x+3}+\frac{2x}{4} \\ \\ \text{Multiplying each fraction by "1":} \\ \\ \frac{1}{x+3} \times \frac{4}{4} +\frac{2x}{4} \times \frac{x+3}{x+3} \\ \\ \frac{4}{4(x+3)} + \frac{2x(x+3)}{4(x+3)} \\ \\ \text{Add across, denominators are the same:} \\ \\ \frac{4+2x(x+3)}{4(x+3)} \\ \\ \text{Expand and simplify numerator:} \\ \\ \frac{2x^2 + 6x + 4}{4(x+3)} \\ \\ \text{We are done!} \end{align*}