Multiply $3$ by $ \dfrac{x}{x^4} $ to get $ \dfrac{ 3x }{ x^4 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $9x^3$ from $ \dfrac{3x}{x^4} $ to get $ \dfrac{ \color{purple}{ -9x^7+3x } }{ x^4 }$.

Step 1: Write $ 9x^3 $ 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 $\color{blue}{x^4}$.

$$ \begin{aligned} \frac{3x}{x^4} -9x^3 & \xlongequal{\text{Step 1}} \frac{3x}{x^4} - \frac{9x^3}{\color{red}{1}} = \frac{ 3x }{ x^4 } - \frac{ 9x^3 \cdot \color{blue}{ x^4 }}{ 1 \cdot \color{blue}{ x^4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x } }{ x^4 } - \frac{ \color{purple}{ 9x^7 } }{ x^4 }=\frac{ \color{purple}{ -9x^7+3x } }{ x^4 } \end{aligned} $$