Subtract $ \dfrac{25}{w} $ from $ 3w^2-w $ to get $ \dfrac{ \color{purple}{ 3w^3-w^2-25 } }{ w }$.

Step 1: Write $ 3w^2-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 $\color{blue}{ w }$.

$$ \begin{aligned} 3w^2-w- \frac{25}{w} & \xlongequal{\text{Step 1}} \frac{3w^2-w}{\color{red}{1}} - \frac{25}{w} = \frac{ \left( 3w^2-w \right) \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} - \frac{ 25 }{ w } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3w^3-w^2 } }{ w } - \frac{ \color{purple}{ 25 } }{ w }=\frac{ \color{purple}{ 3w^3-w^2-25 } }{ w } \end{aligned} $$

Subtract $3$ from $ \dfrac{3w^3-w^2-25}{w} $ to get $ \dfrac{ \color{purple}{ 3w^3-w^2-3w-25 } }{ w }$.

Step 1: Write $ 3 $ 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 $\color{blue}{w}$.

$$ \begin{aligned} \frac{3w^3-w^2-25}{w} -3 & \xlongequal{\text{Step 1}} \frac{3w^3-w^2-25}{w} - \frac{3}{\color{red}{1}} = \frac{ 3w^3-w^2-25 }{ w } - \frac{ 3 \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3w^3-w^2-25 } }{ w } - \frac{ \color{purple}{ 3w } }{ w }=\frac{ \color{purple}{ 3w^3-w^2-3w-25 } }{ w } \end{aligned} $$