Add $10u$ and $ \dfrac{2}{u^2} $ to get $ \dfrac{ \color{purple}{ 10u^3+2 } }{ u^2 }$.

Step 1: Write $ 10u $ 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 first fraction by $\color{blue}{ u^2 }$.

$$ \begin{aligned} 10u+ \frac{2}{u^2} & \xlongequal{\text{Step 1}} \frac{10u}{\color{red}{1}} + \frac{2}{u^2} = \frac{ 10u \cdot \color{blue}{ u^2 }}{ 1 \cdot \color{blue}{ u^2 }} + \frac{ 2 }{ u^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10u^3 } }{ u^2 } + \frac{ \color{purple}{ 2 } }{ u^2 }=\frac{ \color{purple}{ 10u^3+2 } }{ u^2 } \end{aligned} $$

Add $ \dfrac{10u^3+2}{u^2} $ and $ 4u $ to get $ \dfrac{ \color{purple}{ 14u^3+2 } }{ u^2 }$.

Step 1: Write $ 4u $ 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 $\color{blue}{u^2}$.

$$ \begin{aligned} \frac{10u^3+2}{u^2} +4u & \xlongequal{\text{Step 1}} \frac{10u^3+2}{u^2} + \frac{4u}{\color{red}{1}} = \frac{ 10u^3+2 }{ u^2 } + \frac{ 4u \cdot \color{blue}{ u^2 }}{ 1 \cdot \color{blue}{ u^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10u^3+2 } }{ u^2 } + \frac{ \color{purple}{ 4u^3 } }{ u^2 }=\frac{ \color{purple}{ 14u^3+2 } }{ u^2 } \end{aligned} $$

Subtract $49$ from $ \dfrac{14u^3+2}{u^2} $ to get $ \dfrac{ \color{purple}{ 14u^3-49u^2+2 } }{ u^2 }$.

Step 1: Write $ 49 $ 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 second fraction by $\color{blue}{u^2}$.

$$ \begin{aligned} \frac{14u^3+2}{u^2} -49 & \xlongequal{\text{Step 1}} \frac{14u^3+2}{u^2} - \frac{49}{\color{red}{1}} = \frac{ 14u^3+2 }{ u^2 } - \frac{ 49 \cdot \color{blue}{ u^2 }}{ 1 \cdot \color{blue}{ u^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 14u^3+2 } }{ u^2 } - \frac{ \color{purple}{ 49u^2 } }{ u^2 }=\frac{ \color{purple}{ 14u^3-49u^2+2 } }{ u^2 } \end{aligned} $$

Subtract $5u+10$ from $ \dfrac{14u^3-49u^2+2}{u^2} $ to get $ \dfrac{ \color{purple}{ 9u^3-59u^2+2 } }{ u^2 }$.

Step 1: Write $ 5u+10 $ 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 second fraction by $\color{blue}{u^2}$.

$$ \begin{aligned} \frac{14u^3-49u^2+2}{u^2} -5u+10 & \xlongequal{\text{Step 1}} \frac{14u^3-49u^2+2}{u^2} - \frac{5u+10}{\color{red}{1}} = \frac{ 14u^3-49u^2+2 }{ u^2 } - \frac{ \left( 5u+10 \right) \cdot \color{blue}{ u^2 }}{ 1 \cdot \color{blue}{ u^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 14u^3-49u^2+2 } }{ u^2 } - \frac{ \color{purple}{ 5u^3+10u^2 } }{ u^2 }=\frac{ \color{purple}{ 14u^3-49u^2+2 - \left( 5u^3+10u^2 \right) } }{ u^2 } = \\[1ex] &=\frac{ \color{purple}{ 9u^3-59u^2+2 } }{ u^2 } \end{aligned} $$