Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $.

Multiply $ \dfrac{9}{2} $ by $ x $ to get $ \dfrac{ 9x }{ 2 } $.

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.

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

Subtract $15$ from $ \dfrac{9x}{2} $ to get $ \dfrac{ \color{purple}{ 9x-30 } }{ 2 }$.

Step 1: Write $ 15 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} \frac{9x}{2} -15 & \xlongequal{\text{Step 1}} \frac{9x}{2} - \frac{15}{\color{red}{1}} = \frac{ 9x }{ 2 } - \frac{ 15 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x } }{ 2 } - \frac{ \color{purple}{ 30 } }{ 2 }=\frac{ \color{purple}{ 9x-30 } }{ 2 } \end{aligned} $$