Add $ \dfrac{3x^2}{x+5} $ and $ \dfrac{15x}{x+5} $ to get $ \dfrac{ 3x^2 + 15x }{ \color{blue}{ x+5 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{3x^2}{x+5} + \frac{15x}{x+5} & = \frac{3x^2}{\color{blue}{x+5}} + \frac{15x}{\color{blue}{x+5}} =\frac{ 3x^2 + 15x }{ \color{blue}{ x+5 }} \end{aligned} $$

Simplify $ \dfrac{3x^2+15x}{x+5} $ to $ 3x$.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x+5}$.

$$ \begin{aligned} \frac{3x^2+15x}{x+5} & =\frac{ 3x \cdot \color{blue}{ \left( x+5 \right) }}{ 1 \cdot \color{blue}{ \left( x+5 \right) }} = \\[1ex] &= \frac{3x}{1} =3x \end{aligned} $$