Add $ \dfrac{3}{5} $ and $ x $ to get $ \dfrac{ \color{purple}{ 5x+3 } }{ 5 }$.

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

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

Add $ \dfrac{5x+3}{5} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ 5x+48 } }{ 5 }$.

Step 1: Write $ 9 $ 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 $\color{blue}{5}$.

$$ \begin{aligned} \frac{5x+3}{5} +9 & \xlongequal{\text{Step 1}} \frac{5x+3}{5} + \frac{9}{\color{red}{1}} = \frac{ 5x+3 }{ 5 } + \frac{ 9 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x+3 } }{ 5 } + \frac{ \color{purple}{ 45 } }{ 5 }=\frac{ \color{purple}{ 5x+48 } }{ 5 } \end{aligned} $$