Divide $ \dfrac{x}{x} $ by $ 20 $ to get $ \dfrac{ x }{ 20x } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x}{x} }{20} & \xlongequal{\text{Step 1}} \frac{x}{x} \cdot \frac{\color{blue}{1}}{\color{blue}{20}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ x \cdot 20 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 20x } \end{aligned} $$

Multiply $2$ by $ \dfrac{x}{20x} $ to get $ \dfrac{ 2x }{ 20x } $.

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.

$$ \begin{aligned} 2 \cdot \frac{x}{20x} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{x}{20x} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x }{ 1 \cdot 20x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x }{ 20x } \end{aligned} $$

Add $ \dfrac{2x}{20x} $ and $ \dfrac{x}{30} $ to get $ \dfrac{ \color{purple}{ 20x^2+60x } }{ 600x }$.

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}{ 30 }$ and the second by $\color{blue}{ 20x }$.

$$ \begin{aligned} \frac{2x}{20x} + \frac{x}{30} & = \frac{ 2x \cdot \color{blue}{ 30 }}{ 20x \cdot \color{blue}{ 30 }} + \frac{ x \cdot \color{blue}{ 20x }}{ 30 \cdot \color{blue}{ 20x }} = \\[1ex] &=\frac{ \color{purple}{ 60x } }{ 600x } + \frac{ \color{purple}{ 20x^2 } }{ 600x }=\frac{ \color{purple}{ 20x^2+60x } }{ 600x } \end{aligned} $$