Multiply $4$ by $ \dfrac{n}{2n+6} $ to get $ \dfrac{ 4n }{ 2n+6 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{n}{2n+6} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{n}{2n+6} \xlongequal{\text{Step 2}} \frac{ 4 \cdot n }{ 1 \cdot \left( 2n+6 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4n }{ 2n+6 } \end{aligned} $$

Add $ \dfrac{5}{n+5} $ and $ \dfrac{4n}{2n+6} $ to get $ \dfrac{ \color{purple}{ 4n^2+30n+30 } }{ 2n^2+16n+30 }$.

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}{ 2n+6 }$ and the second by $\color{blue}{ n+5 }$.

$$ \begin{aligned} \frac{5}{n+5} + \frac{4n}{2n+6} & = \frac{ 5 \cdot \color{blue}{ \left( 2n+6 \right) }}{ \left( n+5 \right) \cdot \color{blue}{ \left( 2n+6 \right) }} + \frac{ 4n \cdot \color{blue}{ \left( n+5 \right) }}{ \left( 2n+6 \right) \cdot \color{blue}{ \left( n+5 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 10n+30 } }{ 2n^2+6n+10n+30 } + \frac{ \color{purple}{ 4n^2+20n } }{ 2n^2+6n+10n+30 } = \\[1ex] &=\frac{ \color{purple}{ 4n^2+30n+30 } }{ 2n^2+16n+30 } \end{aligned} $$