Multiply $8$ by $ \dfrac{a}{8a+9} $ to get $ \dfrac{ 8a }{ 8a+9 } $.

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.

$$ \begin{aligned} 8 \cdot \frac{a}{8a+9} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{a}{8a+9} \xlongequal{\text{Step 2}} \frac{ 8 \cdot a }{ 1 \cdot \left( 8a+9 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8a }{ 8a+9 } \end{aligned} $$

Add $ \dfrac{8a}{8a+9} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ 32a+27 } }{ 8a+9 }$.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{8a+9}$.

$$ \begin{aligned} \frac{8a}{8a+9} +3 & \xlongequal{\text{Step 1}} \frac{8a}{8a+9} + \frac{3}{\color{red}{1}} = \frac{ 8a }{ 8a+9 } + \frac{ 3 \cdot \color{blue}{ \left( 8a+9 \right) }}{ 1 \cdot \color{blue}{ \left( 8a+9 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8a } }{ 8a+9 } + \frac{ \color{purple}{ 24a+27 } }{ 8a+9 }=\frac{ \color{purple}{ 32a+27 } }{ 8a+9 } \end{aligned} $$