Subtract $2x^3$ from $ \dfrac{x^4+4x^3}{x^4} $ to get $ \dfrac{ \color{purple}{ -2x^7+x^4+4x^3 } }{ x^4 }$.

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

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