Subtract $ \dfrac{3}{c^2-9} $ from $ c $ to get $ \dfrac{ \color{purple}{ c^3-9c-3 } }{ c^2-9 }$.

Step 1: Write $ c $ 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 first fraction by $\color{blue}{ c^2-9 }$.

$$ \begin{aligned} c- \frac{3}{c^2-9} & \xlongequal{\text{Step 1}} \frac{c}{\color{red}{1}} - \frac{3}{c^2-9} = \frac{ c \cdot \color{blue}{ \left( c^2-9 \right) }}{ 1 \cdot \color{blue}{ \left( c^2-9 \right) }} - \frac{ 3 }{ c^2-9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ c^3-9c } }{ c^2-9 } - \frac{ \color{purple}{ 3 } }{ c^2-9 }=\frac{ \color{purple}{ c^3-9c-3 } }{ c^2-9 } \end{aligned} $$