Multiply $ \dfrac{7}{w} $ by $ 2 $ to get $ \dfrac{ 14 }{ w } $.

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.

$$ \begin{aligned} \frac{7}{w} \cdot 2 & \xlongequal{\text{Step 1}} \frac{7}{w} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot 2 }{ w \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 14 }{ w } \end{aligned} $$

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

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

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

Subtract $12w$ from $ \dfrac{w^2-14}{w} $ to get $ \dfrac{ \color{purple}{ -11w^2-14 } }{ w }$.

Step 1: Write $ 12w $ 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 $\color{blue}{w}$.

$$ \begin{aligned} \frac{w^2-14}{w} -12w & \xlongequal{\text{Step 1}} \frac{w^2-14}{w} - \frac{12w}{\color{red}{1}} = \frac{ w^2-14 }{ w } - \frac{ 12w \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ w^2-14 } }{ w } - \frac{ \color{purple}{ 12w^2 } }{ w }=\frac{ \color{purple}{ -11w^2-14 } }{ w } \end{aligned} $$

Add $ \dfrac{-11w^2-14}{w} $ and $ 35 $ to get $ \dfrac{ \color{purple}{ -11w^2+35w-14 } }{ w }$.

Step 1: Write $ 35 $ 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 $\color{blue}{w}$.

$$ \begin{aligned} \frac{-11w^2-14}{w} +35 & \xlongequal{\text{Step 1}} \frac{-11w^2-14}{w} + \frac{35}{\color{red}{1}} = \frac{ -11w^2-14 }{ w } + \frac{ 35 \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -11w^2-14 } }{ w } + \frac{ \color{purple}{ 35w } }{ w }=\frac{ \color{purple}{ -11w^2+35w-14 } }{ w } \end{aligned} $$