Divide $ \dfrac{2}{u} $ by $ u $ to get $ \dfrac{ 2 }{ u^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.

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

Divide $ \dfrac{2}{u^2} $ by $ 4 $ to get $ \dfrac{ 2 }{ 4u^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.

$$ \begin{aligned} \frac{ \frac{2}{u^2} }{4} & \xlongequal{\text{Step 1}} \frac{2}{u^2} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot 1 }{ u^2 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 4u^2 } \end{aligned} $$

Add $ \dfrac{2}{4u^2} $ and $ \dfrac{1}{u} $ to get $ \dfrac{ \color{purple}{ 4u^2+2u } }{ 4u^3 }$.

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}{ u }$ and the second by $\color{blue}{ 4u^2 }$.

$$ \begin{aligned} \frac{2}{4u^2} + \frac{1}{u} & = \frac{ 2 \cdot \color{blue}{ u }}{ 4u^2 \cdot \color{blue}{ u }} + \frac{ 1 \cdot \color{blue}{ 4u^2 }}{ u \cdot \color{blue}{ 4u^2 }} = \\[1ex] &=\frac{ \color{purple}{ 2u } }{ 4u^3 } + \frac{ \color{purple}{ 4u^2 } }{ 4u^3 }=\frac{ \color{purple}{ 4u^2+2u } }{ 4u^3 } \end{aligned} $$