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

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

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

Subtract $4$ from $ \dfrac{x^3-2}{x^2} $ to get $ \dfrac{ \color{purple}{ x^3-4x^2-2 } }{ x^2 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^3-2}{x^2} -4 & \xlongequal{\text{Step 1}} \frac{x^3-2}{x^2} - \frac{4}{\color{red}{1}} = \frac{ x^3-2 }{ x^2 } - \frac{ 4 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^3-2 } }{ x^2 } - \frac{ \color{purple}{ 4x^2 } }{ x^2 }=\frac{ \color{purple}{ x^3-4x^2-2 } }{ x^2 } \end{aligned} $$