Add $ \dfrac{4}{3} $ and $ \dfrac{3}{3k^2+15k} $ to get $ \dfrac{ \color{purple}{ 12k^2+60k+9 } }{ 9k^2+45k }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3k^2+15k }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{4}{3} + \frac{3}{3k^2+15k} & = \frac{ 4 \cdot \color{blue}{ \left( 3k^2+15k \right) }}{ 3 \cdot \color{blue}{ \left( 3k^2+15k \right) }} + \frac{ 3 \cdot \color{blue}{ 3 }}{ \left( 3k^2+15k \right) \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 12k^2+60k } }{ 9k^2+45k } + \frac{ \color{purple}{ 9 } }{ 9k^2+45k }=\frac{ \color{purple}{ 12k^2+60k+9 } }{ 9k^2+45k } \end{aligned} $$