Multiply $ \dfrac{9}{4} $ by $ x $ to get $ \dfrac{ 9x }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9}{4} \cdot x & \xlongequal{\text{Step 1}} \frac{9}{4} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 9x }{ 4 } \end{aligned} $$

Multiply $ \dfrac{9x}{4} $ by $ 8 $ to get $ \dfrac{ 72x }{ 4 } $.

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.

$$ \begin{aligned} \frac{9x}{4} \cdot 8 & \xlongequal{\text{Step 1}} \frac{9x}{4} \cdot \frac{8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x \cdot 8 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 72x }{ 4 } \end{aligned} $$

Add $9x$ and $ \dfrac{72x}{4} $ to get $ \dfrac{ \color{purple}{ 108x } }{ 4 }$.

Step 1: Write $ 9x $ 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 first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} 9x+ \frac{72x}{4} & \xlongequal{\text{Step 1}} \frac{9x}{\color{red}{1}} + \frac{72x}{4} = \frac{ 9x \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} + \frac{ 72x }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 36x } }{ 4 } + \frac{ \color{purple}{ 72x } }{ 4 }=\frac{ \color{purple}{ 108x } }{ 4 } \end{aligned} $$