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

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

$$ \begin{aligned} x+ \frac{20}{x-4} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} + \frac{20}{x-4} = \frac{ x \cdot \color{blue}{ \left( x-4 \right) }}{ 1 \cdot \color{blue}{ \left( x-4 \right) }} + \frac{ 20 }{ x-4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^2-4x } }{ x-4 } + \frac{ \color{purple}{ 20 } }{ x-4 }=\frac{ \color{purple}{ x^2-4x+20 } }{ x-4 } \end{aligned} $$