Add $ \dfrac{23}{x} $ and $ 2 $ to get $ \dfrac{ \color{purple}{ 2x+23 } }{ x }$.

Step 1: Write $ 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 second fraction by $\color{blue}{x}$.

$$ \begin{aligned} \frac{23}{x} +2 & \xlongequal{\text{Step 1}} \frac{23}{x} + \frac{2}{\color{red}{1}} = \frac{ 23 }{ x } + \frac{ 2 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 23 } }{ x } + \frac{ \color{purple}{ 2x } }{ x }=\frac{ \color{purple}{ 2x+23 } }{ x } \end{aligned} $$

Subtract $ \dfrac{4}{x} $ from $ \dfrac{2x+23}{x} $ to get $ \dfrac{2x+19}{x} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{2x+23}{x} - \frac{4}{x} & = \frac{2x+23}{\color{blue}{x}} - \frac{4}{\color{blue}{x}} =\frac{ 2x+23 - 4 }{ \color{blue}{ x }} = \\[1ex] &= \frac{2x+19}{x} \end{aligned} $$