$$ 2 x \cdot 2 = 4 x $$

Combine like terms:

$$ \color{blue}{-4x} + \color{blue}{8x} = \color{blue}{4x} $$

Subtract $ \dfrac{8}{x} $ from $ 4x $ to get $ \dfrac{ \color{purple}{ 4x^2-8 } }{ x }$.

Step 1: Write $ 4x $ 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 $\color{blue}{ x }$.

$$ \begin{aligned} 4x- \frac{8}{x} & \xlongequal{\text{Step 1}} \frac{4x}{\color{red}{1}} - \frac{8}{x} = \frac{ 4x \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} - \frac{ 8 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^2 } }{ x } - \frac{ \color{purple}{ 8 } }{ x }=\frac{ \color{purple}{ 4x^2-8 } }{ x } \end{aligned} $$

Subtract $2$ from $ \dfrac{4x^2-8}{x} $ to get $ \dfrac{ \color{purple}{ 4x^2-2x-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 $\color{blue}{x}$.

$$ \begin{aligned} \frac{4x^2-8}{x} -2 & \xlongequal{\text{Step 1}} \frac{4x^2-8}{x} - \frac{2}{\color{red}{1}} = \frac{ 4x^2-8 }{ x } - \frac{ 2 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^2-8 } }{ x } - \frac{ \color{purple}{ 2x } }{ x }=\frac{ \color{purple}{ 4x^2-2x-8 } }{ x } \end{aligned} $$