Add $a+3$ and $ \dfrac{5}{4} $ to get $ \dfrac{ \color{purple}{ 4a+17 } }{ 4 }$.

Step 1: Write $ a+3 $ 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 $\color{blue}{ 4 }$.

$$ \begin{aligned} a+3+ \frac{5}{4} & \xlongequal{\text{Step 1}} \frac{a+3}{\color{red}{1}} + \frac{5}{4} = \frac{ \left( a+3 \right) \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} + \frac{ 5 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4a+12 } }{ 4 } + \frac{ \color{purple}{ 5 } }{ 4 }=\frac{ \color{purple}{ 4a+17 } }{ 4 } \end{aligned} $$