Subtract $w$ from $ \dfrac{100}{c} $ to get $ \dfrac{ \color{purple}{ -cw+100 } }{ c }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{c}$.

$$ \begin{aligned} \frac{100}{c} -w & \xlongequal{\text{Step 1}} \frac{100}{c} - \frac{w}{\color{red}{1}} = \frac{ 100 }{ c } - \frac{ w \cdot \color{blue}{ c }}{ 1 \cdot \color{blue}{ c }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 100 } }{ c } - \frac{ \color{purple}{ cw } }{ c }=\frac{ \color{purple}{ -cw+100 } }{ c } \end{aligned} $$

Add $ \dfrac{-cw+100}{c} $ and $ \dfrac{w}{c} $ to get $ \dfrac{-cw+w+100}{c} $.

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

$$ \begin{aligned} \frac{-cw+100}{c} + \frac{w}{c} & = \frac{-cw+100}{\color{blue}{c}} + \frac{w}{\color{blue}{c}} =\frac{ -cw+100 + w }{ \color{blue}{ c }} = \\[1ex] &= \frac{-cw+w+100}{c} \end{aligned} $$