Multiply $8$ by $ \dfrac{x}{7x+8} $ to get $ \dfrac{ 8x }{ 7x+8 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{x}{7x+8} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{x}{7x+8} \xlongequal{\text{Step 2}} \frac{ 8 \cdot x }{ 1 \cdot \left( 7x+8 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x }{ 7x+8 } \end{aligned} $$

Add $ \dfrac{x}{7x+8} $ and $ \dfrac{8x}{7x+8} $ to get $ \dfrac{9x}{7x+8} $.

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

$$ \begin{aligned} \frac{x}{7x+8} + \frac{8x}{7x+8} & = \frac{x}{\color{blue}{7x+8}} + \frac{8x}{\color{blue}{7x+8}} =\frac{ x + 8x }{ \color{blue}{ 7x+8 }} = \\[1ex] &= \frac{9x}{7x+8} \end{aligned} $$