Add $ \dfrac{10695408000+i}{18584961} $ and $ 6i $ to get $ \dfrac{ \color{purple}{ 111509767i+10695408000 } }{ 18584961 }$.

Step 1: Write $ 6i $ 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 $\color{blue}{18584961}$.

$$ \begin{aligned} \frac{10695408000+i}{18584961} +6i & \xlongequal{\text{Step 1}} \frac{10695408000+i}{18584961} + \frac{6i}{\color{red}{1}} = \frac{ 10695408000+i }{ 18584961 } + \frac{ 6i \cdot \color{blue}{ 18584961 }}{ 1 \cdot \color{blue}{ 18584961 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10695408000+i } }{ 18584961 } + \frac{ \color{purple}{ 111509766i } }{ 18584961 } = \\[1ex] &=\frac{ \color{purple}{ 111509767i+10695408000 } }{ 18584961 } \end{aligned} $$

Add $ \dfrac{i+10695408000}{18584961} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ i+10862672649 } }{ 18584961 }$.

Step 1: Write $ 9 $ 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 $\color{blue}{18584961}$.

$$ \begin{aligned} \frac{i+10695408000}{18584961} +9 & \xlongequal{\text{Step 1}} \frac{i+10695408000}{18584961} + \frac{9}{\color{red}{1}} = \frac{ i+10695408000 }{ 18584961 } + \frac{ 9 \cdot \color{blue}{ 18584961 }}{ 1 \cdot \color{blue}{ 18584961 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ i+10695408000 } }{ 18584961 } + \frac{ \color{purple}{ 167264649 } }{ 18584961 } = \\[1ex] &=\frac{ \color{purple}{ i+10862672649 } }{ 18584961 } \end{aligned} $$