Multiply $12$ by $ \dfrac{x}{x^2} $ to get $ \dfrac{ 12x }{ x^2 } $.

Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 12 \cdot \frac{x}{x^2} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{x}{x^2} \xlongequal{\text{Step 2}} \frac{ 12 \cdot x }{ 1 \cdot x^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x }{ x^2 } \end{aligned} $$

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

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 $\color{blue}{ x^2 }$.

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

Subtract $3x$ from $ \dfrac{2x^4-12x}{x^2} $ to get $ \dfrac{ \color{purple}{ 2x^4-3x^3-12x } }{ x^2 }$.

Step 1: Write $ 3x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{2x^4-12x}{x^2} -3x & \xlongequal{\text{Step 1}} \frac{2x^4-12x}{x^2} - \frac{3x}{\color{red}{1}} = \frac{ 2x^4-12x }{ x^2 } - \frac{ 3x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4-12x } }{ x^2 } - \frac{ \color{purple}{ 3x^3 } }{ x^2 }=\frac{ \color{purple}{ 2x^4-3x^3-12x } }{ x^2 } \end{aligned} $$

Subtract $18$ from $ \dfrac{2x^4-3x^3-12x}{x^2} $ to get $ \dfrac{ \color{purple}{ 2x^4-3x^3-18x^2-12x } }{ x^2 }$.

Step 1: Write $ 18 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{2x^4-3x^3-12x}{x^2} -18 & \xlongequal{\text{Step 1}} \frac{2x^4-3x^3-12x}{x^2} - \frac{18}{\color{red}{1}} = \frac{ 2x^4-3x^3-12x }{ x^2 } - \frac{ 18 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4-3x^3-12x } }{ x^2 } - \frac{ \color{purple}{ 18x^2 } }{ x^2 }=\frac{ \color{purple}{ 2x^4-3x^3-18x^2-12x } }{ x^2 } \end{aligned} $$