Multiply $30$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 30x }{ 4 } $.

Step 1: Write $ 30 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 30 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{30}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 30 \cdot x }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x }{ 4 } \end{aligned} $$

Multiply $ \dfrac{30x}{4} $ by $ x^4 $ to get $ \dfrac{ 30x^5 }{ 4 } $.

Step 1: Write $ x^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{30x}{4} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{30x}{4} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30x \cdot x^4 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^5 }{ 4 } \end{aligned} $$

Add $20x^2$ and $ \dfrac{30x^5}{4} $ to get $ \dfrac{ \color{purple}{ 30x^5+80x^2 } }{ 4 }$.

Step 1: Write $ 20x^2 $ 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 first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} 20x^2+ \frac{30x^5}{4} & \xlongequal{\text{Step 1}} \frac{20x^2}{\color{red}{1}} + \frac{30x^5}{4} = \frac{ 20x^2 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} + \frac{ 30x^5 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 80x^2 } }{ 4 } + \frac{ \color{purple}{ 30x^5 } }{ 4 }=\frac{ \color{purple}{ 30x^5+80x^2 } }{ 4 } \end{aligned} $$

Add $ \dfrac{30x^5+80x^2}{4} $ and $ 6x^3 $ to get $ \dfrac{ \color{purple}{ 30x^5+24x^3+80x^2 } }{ 4 }$.

Step 1: Write $ 6x^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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{30x^5+80x^2}{4} +6x^3 & \xlongequal{\text{Step 1}} \frac{30x^5+80x^2}{4} + \frac{6x^3}{\color{red}{1}} = \frac{ 30x^5+80x^2 }{ 4 } + \frac{ 6x^3 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 30x^5+80x^2 } }{ 4 } + \frac{ \color{purple}{ 24x^3 } }{ 4 }=\frac{ \color{purple}{ 30x^5+24x^3+80x^2 } }{ 4 } \end{aligned} $$