Multiply $3$ by $ \dfrac{i}{n} $ to get $ \dfrac{ 3i }{ n } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $1$ and $ \dfrac{3i}{n} $ to get $ \dfrac{ \color{purple}{ 3i+n } }{ n }$.

Step 1: Write $ 1 $ 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 $\color{blue}{ n }$.

$$ \begin{aligned} 1+ \frac{3i}{n} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{3i}{n} = \frac{ 1 \cdot \color{blue}{ n }}{ 1 \cdot \color{blue}{ n }} + \frac{ 3i }{ n } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ n } }{ n } + \frac{ \color{purple}{ 3i } }{ n }=\frac{ \color{purple}{ 3i+n } }{ n } \end{aligned} $$

Multiply $2$ by $ \dfrac{3i+n}{n} $ to get $ \dfrac{ 6i+2n }{ n } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{3i+n}{n} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{3i+n}{n} \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( 3i+n \right) }{ 1 \cdot n } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6i+2n }{ n } \end{aligned} $$