Use the distributive property.

Add $ \dfrac{x}{x^4} $ and $ x^3 $ to get $ \dfrac{ \color{purple}{ x^7+x } }{ x^4 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{x^4}$.

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

Multiply $ \dfrac{x^7+x}{x^4} $ by $ 2 $ to get $ \dfrac{ 2x^7+2x }{ x^4 } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^7+x}{x^4} \cdot 2 & \xlongequal{\text{Step 1}} \frac{x^7+x}{x^4} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^7+x \right) \cdot 2 }{ x^4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^7+2x }{ x^4 } \end{aligned} $$