Multiply $ \dfrac{13}{u} $ by $ 2 $ to get $ \dfrac{ 26 }{ u } $.

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.

$$ \begin{aligned} \frac{13}{u} \cdot 2 & \xlongequal{\text{Step 1}} \frac{13}{u} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 13 \cdot 2 }{ u \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 26 }{ u } \end{aligned} $$

Subtract $ \dfrac{26}{u} $ from $ u $ to get $ \dfrac{ \color{purple}{ u^2-26 } }{ u }$.

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

$$ \begin{aligned} u- \frac{26}{u} & \xlongequal{\text{Step 1}} \frac{u}{\color{red}{1}} - \frac{26}{u} = \frac{ u \cdot \color{blue}{ u }}{ 1 \cdot \color{blue}{ u }} - \frac{ 26 }{ u } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ u^2 } }{ u } - \frac{ \color{purple}{ 26 } }{ u }=\frac{ \color{purple}{ u^2-26 } }{ u } \end{aligned} $$

Subtract $15u$ from $ \dfrac{u^2-26}{u} $ to get $ \dfrac{ \color{purple}{ -14u^2-26 } }{ u }$.

Step 1: Write $ 15u $ 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 $\color{blue}{u}$.

$$ \begin{aligned} \frac{u^2-26}{u} -15u & \xlongequal{\text{Step 1}} \frac{u^2-26}{u} - \frac{15u}{\color{red}{1}} = \frac{ u^2-26 }{ u } - \frac{ 15u \cdot \color{blue}{ u }}{ 1 \cdot \color{blue}{ u }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ u^2-26 } }{ u } - \frac{ \color{purple}{ 15u^2 } }{ u }=\frac{ \color{purple}{ -14u^2-26 } }{ u } \end{aligned} $$

Add $ \dfrac{-14u^2-26}{u} $ and $ 26 $ to get $ \dfrac{ \color{purple}{ -14u^2+26u-26 } }{ u }$.

Step 1: Write $ 26 $ 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 $\color{blue}{u}$.

$$ \begin{aligned} \frac{-14u^2-26}{u} +26 & \xlongequal{\text{Step 1}} \frac{-14u^2-26}{u} + \frac{26}{\color{red}{1}} = \frac{ -14u^2-26 }{ u } + \frac{ 26 \cdot \color{blue}{ u }}{ 1 \cdot \color{blue}{ u }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -14u^2-26 } }{ u } + \frac{ \color{purple}{ 26u } }{ u }=\frac{ \color{purple}{ -14u^2+26u-26 } }{ u } \end{aligned} $$