Add $3c-10$ and $ \dfrac{3}{9c+2} $ to get $ \dfrac{ \color{purple}{ 27c^2-84c-17 } }{ 9c+2 }$.

Step 1: Write $ 3c-10 $ 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 $\color{blue}{ 9c+2 }$.

$$ \begin{aligned} 3c-10+ \frac{3}{9c+2} & \xlongequal{\text{Step 1}} \frac{3c-10}{\color{red}{1}} + \frac{3}{9c+2} = \frac{ \left( 3c-10 \right) \cdot \color{blue}{ \left( 9c+2 \right) }}{ 1 \cdot \color{blue}{ \left( 9c+2 \right) }} + \frac{ 3 }{ 9c+2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 27c^2+6c-90c-20 } }{ 9c+2 } + \frac{ \color{purple}{ 3 } }{ 9c+2 }=\frac{ \color{purple}{ 27c^2-84c-17 } }{ 9c+2 } \end{aligned} $$