Add $ \dfrac{2}{q^3} $ and $ 7r $ to get $ \dfrac{ \color{purple}{ 7q^3r+2 } }{ q^3 }$.

Step 1: Write $ 7r $ 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 $\color{blue}{q^3}$.

$$ \begin{aligned} \frac{2}{q^3} +7r & \xlongequal{\text{Step 1}} \frac{2}{q^3} + \frac{7r}{\color{red}{1}} = \frac{ 2 }{ q^3 } + \frac{ 7r \cdot \color{blue}{ q^3 }}{ 1 \cdot \color{blue}{ q^3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2 } }{ q^3 } + \frac{ \color{purple}{ 7q^3r } }{ q^3 }=\frac{ \color{purple}{ 7q^3r+2 } }{ q^3 } \end{aligned} $$

Add $ \dfrac{7q^3r+2}{q^3} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ 7q^3r+6q^3+2 } }{ q^3 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{q^3}$.

$$ \begin{aligned} \frac{7q^3r+2}{q^3} +6 & \xlongequal{\text{Step 1}} \frac{7q^3r+2}{q^3} + \frac{6}{\color{red}{1}} = \frac{ 7q^3r+2 }{ q^3 } + \frac{ 6 \cdot \color{blue}{ q^3 }}{ 1 \cdot \color{blue}{ q^3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7q^3r+2 } }{ q^3 } + \frac{ \color{purple}{ 6q^3 } }{ q^3 }=\frac{ \color{purple}{ 7q^3r+6q^3+2 } }{ q^3 } \end{aligned} $$