Subtract $ \dfrac{8}{x} $ from $ 2x^2 $ to get $ \dfrac{ \color{purple}{ 2x^3-8 } }{ x }$.

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

$$ \begin{aligned} 2x^2- \frac{8}{x} & \xlongequal{\text{Step 1}} \frac{2x^2}{\color{red}{1}} - \frac{8}{x} = \frac{ 2x^2 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} - \frac{ 8 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^3 } }{ x } - \frac{ \color{purple}{ 8 } }{ x }=\frac{ \color{purple}{ 2x^3-8 } }{ x } \end{aligned} $$

Subtract $2$ from $ \dfrac{2x^3-8}{x} $ to get $ \dfrac{ \color{purple}{ 2x^3-2x-8 } }{ x }$.

Step 1: Write $ 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 second fraction by $\color{blue}{x}$.

$$ \begin{aligned} \frac{2x^3-8}{x} -2 & \xlongequal{\text{Step 1}} \frac{2x^3-8}{x} - \frac{2}{\color{red}{1}} = \frac{ 2x^3-8 }{ x } - \frac{ 2 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^3-8 } }{ x } - \frac{ \color{purple}{ 2x } }{ x }=\frac{ \color{purple}{ 2x^3-2x-8 } }{ x } \end{aligned} $$