Add $x-3$ and $ \dfrac{4}{w} $ to get $ \dfrac{ \color{purple}{ wx-3w+4 } }{ w }$.

Step 1: Write $ x-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 first fraction by $\color{blue}{ w }$.

$$ \begin{aligned} x-3+ \frac{4}{w} & \xlongequal{\text{Step 1}} \frac{x-3}{\color{red}{1}} + \frac{4}{w} = \frac{ \left( x-3 \right) \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} + \frac{ 4 }{ w } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ wx-3w } }{ w } + \frac{ \color{purple}{ 4 } }{ w }=\frac{ \color{purple}{ wx-3w+4 } }{ w } \end{aligned} $$