Multiply $2$ by $ \dfrac{a}{a^2} $ to get $ \dfrac{ 2a }{ a^2 } $.

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.

$$ \begin{aligned} 2 \cdot \frac{a}{a^2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{a}{a^2} \xlongequal{\text{Step 2}} \frac{ 2 \cdot a }{ 1 \cdot a^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a }{ a^2 } \end{aligned} $$

Multiply $ \dfrac{2a}{a^2} $ by $ b $ to get $ \dfrac{ 2ab }{ a^2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2a}{a^2} \cdot b & \xlongequal{\text{Step 1}} \frac{2a}{a^2} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2a \cdot b }{ a^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ab }{ a^2 } \end{aligned} $$

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

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 $\color{blue}{ a^2 }$.

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