Add $ \dfrac{4}{5} $ and $ 3c $ to get $ \dfrac{ \color{purple}{ 15c+4 } }{ 5 }$.

Step 1: Write $ 3c $ 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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{4}{5} +3c & \xlongequal{\text{Step 1}} \frac{4}{5} + \frac{3c}{\color{red}{1}} = \frac{ 4 }{ 5 } + \frac{ 3c \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4 } }{ 5 } + \frac{ \color{purple}{ 15c } }{ 5 }=\frac{ \color{purple}{ 15c+4 } }{ 5 } \end{aligned} $$

Subtract $10$ from $ \dfrac{15c+4}{5} $ to get $ \dfrac{ \color{purple}{ 15c-46 } }{ 5 }$.

Step 1: Write $ 10 $ 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 $\color{blue}{5}$.

$$ \begin{aligned} \frac{15c+4}{5} -10 & \xlongequal{\text{Step 1}} \frac{15c+4}{5} - \frac{10}{\color{red}{1}} = \frac{ 15c+4 }{ 5 } - \frac{ 10 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 15c+4 } }{ 5 } - \frac{ \color{purple}{ 50 } }{ 5 }=\frac{ \color{purple}{ 15c-46 } }{ 5 } \end{aligned} $$