Multiply $7$ by $ \dfrac{x}{3} $ to get $ \dfrac{ 7x }{ 3 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{x}{3} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x}{3} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 7x }{ 3 } \end{aligned} $$

Multiply $ \dfrac{7x}{3} $ by $ x^2 $ to get $ \dfrac{ 7x^3 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{2}{x} $ from $ \dfrac{7x^3}{3} $ to get $ \dfrac{ \color{purple}{ 7x^4-6 } }{ 3x }$.

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 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{7x^3}{3} - \frac{2}{x} & = \frac{ 7x^3 \cdot \color{blue}{ x }}{ 3 \cdot \color{blue}{ x }} - \frac{ 2 \cdot \color{blue}{ 3 }}{ x \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 7x^4 } }{ 3x } - \frac{ \color{purple}{ 6 } }{ 3x }=\frac{ \color{purple}{ 7x^4-6 } }{ 3x } \end{aligned} $$

Add $ \dfrac{7x^4-6}{3x} $ and $ 4 $ to get $ \dfrac{ \color{purple}{ 7x^4+12x-6 } }{ 3x }$.

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

$$ \begin{aligned} \frac{7x^4-6}{3x} +4 & \xlongequal{\text{Step 1}} \frac{7x^4-6}{3x} + \frac{4}{\color{red}{1}} = \frac{ 7x^4-6 }{ 3x } + \frac{ 4 \cdot \color{blue}{ 3x }}{ 1 \cdot \color{blue}{ 3x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x^4-6 } }{ 3x } + \frac{ \color{purple}{ 12x } }{ 3x }=\frac{ \color{purple}{ 7x^4+12x-6 } }{ 3x } \end{aligned} $$