Subtract $ \dfrac{2}{x} $ from $ x^4+12x $ to get $ \dfrac{ \color{purple}{ x^5+12x^2-2 } }{ x }$.

Step 1: Write $ x^4+12x $ 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 $\color{blue}{ x }$.

$$ \begin{aligned} x^4+12x- \frac{2}{x} & \xlongequal{\text{Step 1}} \frac{x^4+12x}{\color{red}{1}} - \frac{2}{x} = \frac{ \left( x^4+12x \right) \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} - \frac{ 2 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^5+12x^2 } }{ x } - \frac{ \color{purple}{ 2 } }{ x }=\frac{ \color{purple}{ x^5+12x^2-2 } }{ x } \end{aligned} $$

Subtract $1$ from $ \dfrac{x^5+12x^2-2}{x} $ to get $ \dfrac{ \color{purple}{ x^5+12x^2-x-2 } }{ x }$.

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

$$ \begin{aligned} \frac{x^5+12x^2-2}{x} -1 & \xlongequal{\text{Step 1}} \frac{x^5+12x^2-2}{x} - \frac{1}{\color{red}{1}} = \frac{ x^5+12x^2-2 }{ x } - \frac{ 1 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^5+12x^2-2 } }{ x } - \frac{ \color{purple}{ x } }{ x }=\frac{ \color{purple}{ x^5+12x^2-x-2 } }{ x } \end{aligned} $$