Add $ \dfrac{2}{a} $ and $ \dfrac{7}{b} $ to get $ \dfrac{ \color{purple}{ 7a+2b } }{ ab }$.

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}{ b }$ and the second by $\color{blue}{ a }$.

$$ \begin{aligned} \frac{2}{a} + \frac{7}{b} & = \frac{ 2 \cdot \color{blue}{ b }}{ a \cdot \color{blue}{ b }} + \frac{ 7 \cdot \color{blue}{ a }}{ b \cdot \color{blue}{ a }} = \\[1ex] &=\frac{ \color{purple}{ 2b } }{ ab } + \frac{ \color{purple}{ 7a } }{ ab }=\frac{ \color{purple}{ 7a+2b } }{ ab } \end{aligned} $$

Divide $ \dfrac{7a+2b}{ab} $ by $ b $ to get $ \dfrac{ 7a+2b }{ ab^2 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{7a+2b}{ab} }{b} & \xlongequal{\text{Step 1}} \frac{7a+2b}{ab} \cdot \frac{\color{blue}{1}}{\color{blue}{b}} \xlongequal{\text{Step 2}} \frac{ \left( 7a+2b \right) \cdot 1 }{ ab \cdot b } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7a+2b }{ ab^2 } \end{aligned} $$