Multiply $9$ by $ \dfrac{i}{6} $ to get $ \dfrac{ 9i }{ 6 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{i}{6} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{i}{6} \xlongequal{\text{Step 2}} \frac{ 9 \cdot i }{ 1 \cdot 6 } \xlongequal{\text{Step 3}} \frac{ 9i }{ 6 } \end{aligned} $$

Subtract $5i$ from $ \dfrac{9i}{6} $ to get $ \dfrac{ \color{purple}{ -21i } }{ 6 }$.

Step 1: Write $ 5i $ 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 $\color{blue}{6}$.

$$ \begin{aligned} \frac{9i}{6} -5i & \xlongequal{\text{Step 1}} \frac{9i}{6} - \frac{5i}{\color{red}{1}} = \frac{ 9i }{ 6 } - \frac{ 5i \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9i } }{ 6 } - \frac{ \color{purple}{ 30i } }{ 6 }=\frac{ \color{purple}{ -21i } }{ 6 } \end{aligned} $$