Add $ \dfrac{5}{2x+8} $ and $ \dfrac{7}{3x+12} $ to get $ \dfrac{ \color{purple}{ 29 } }{ 6x+24 }$.

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}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{5}{2x+8} + \frac{7}{3x+12} & = \frac{ 5 \cdot \color{blue}{ 3 }}{ \left( 2x+8 \right) \cdot \color{blue}{ 3 }} + \frac{ 7 \cdot \color{blue}{ 2 }}{ \left( 3x+12 \right) \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 15 } }{ 6x+24 } + \frac{ \color{purple}{ 14 } }{ 6x+24 }=\frac{ \color{purple}{ 29 } }{ 6x+24 } \end{aligned} $$