Multiply $7$ by $ \dfrac{x}{x+4} $ to get $ \dfrac{ 7x }{ x+4 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{x}{x+4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x}{x+4} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 1 \cdot \left( x+4 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x }{ x+4 } \end{aligned} $$

Multiply $11$ by $ \dfrac{x}{x+5} $ to get $ \dfrac{ 11x }{ x+5 } $.

Step 1: Write $ 11 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 11 \cdot \frac{x}{x+5} & \xlongequal{\text{Step 1}} \frac{11}{\color{red}{1}} \cdot \frac{x}{x+5} \xlongequal{\text{Step 2}} \frac{ 11 \cdot x }{ 1 \cdot \left( x+5 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 11x }{ x+5 } \end{aligned} $$

Add $ \dfrac{7x}{x+4} $ and $ \dfrac{11x}{x+5} $ to get $ \dfrac{ \color{purple}{ 18x^2+79x } }{ x^2+9x+20 }$.

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}{ x+5 }$ and the second by $\color{blue}{ x+4 }$.

$$ \begin{aligned} \frac{7x}{x+4} + \frac{11x}{x+5} & = \frac{ 7x \cdot \color{blue}{ \left( x+5 \right) }}{ \left( x+4 \right) \cdot \color{blue}{ \left( x+5 \right) }} + \frac{ 11x \cdot \color{blue}{ \left( x+4 \right) }}{ \left( x+5 \right) \cdot \color{blue}{ \left( x+4 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 7x^2+35x } }{ x^2+5x+4x+20 } + \frac{ \color{purple}{ 11x^2+44x } }{ x^2+5x+4x+20 } = \\[1ex] &=\frac{ \color{purple}{ 18x^2+79x } }{ x^2+9x+20 } \end{aligned} $$