Subtract $ \dfrac{36}{u} $ from $ u^2 $ to get $ \dfrac{ \color{purple}{ u^3-36 } }{ u }$.

Step 1: Write $ u^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ u }$.

$$ \begin{aligned} u^2- \frac{36}{u} & \xlongequal{\text{Step 1}} \frac{u^2}{\color{red}{1}} - \frac{36}{u} = \frac{ u^2 \cdot \color{blue}{ u }}{ 1 \cdot \color{blue}{ u }} - \frac{ 36 }{ u } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ u^3 } }{ u } - \frac{ \color{purple}{ 36 } }{ u }=\frac{ \color{purple}{ u^3-36 } }{ u } \end{aligned} $$

Add $ \dfrac{u^3-36}{u} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ u^3+6u-36 } }{ u }$.

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 $\color{blue}{u}$.

$$ \begin{aligned} \frac{u^3-36}{u} +6 & \xlongequal{\text{Step 1}} \frac{u^3-36}{u} + \frac{6}{\color{red}{1}} = \frac{ u^3-36 }{ u } + \frac{ 6 \cdot \color{blue}{ u }}{ 1 \cdot \color{blue}{ u }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ u^3-36 } }{ u } + \frac{ \color{purple}{ 6u } }{ u }=\frac{ \color{purple}{ u^3+6u-36 } }{ u } \end{aligned} $$