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

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 $\color{blue}{ x }$.

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

Subtract $6$ from $ \dfrac{x^2-2}{x} $ to get $ \dfrac{ \color{purple}{ x^2-6x-2 } }{ x }$.

Step 1: Write $ 6 $ 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 $\color{blue}{x}$.

$$ \begin{aligned} \frac{x^2-2}{x} -6 & \xlongequal{\text{Step 1}} \frac{x^2-2}{x} - \frac{6}{\color{red}{1}} = \frac{ x^2-2 }{ x } - \frac{ 6 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^2-2 } }{ x } - \frac{ \color{purple}{ 6x } }{ x }=\frac{ \color{purple}{ x^2-6x-2 } }{ x } \end{aligned} $$