Add $c$ and $ \dfrac{c}{c+2} $ to get $ \dfrac{ \color{purple}{ c^2+3c } }{ c+2 }$.

Step 1: Write $ c $ 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 $\color{blue}{ c+2 }$.

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