Add $ \dfrac{5}{y} $ and $ \dfrac{3}{y} $ to get $ \dfrac{8}{y} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{5}{y} + \frac{3}{y} & = \frac{5}{\color{blue}{y}} + \frac{3}{\color{blue}{y}} =\frac{ 5 + 3 }{ \color{blue}{ y }} = \\[1ex] &= \frac{8}{y} \end{aligned} $$

Add $ \dfrac{8}{y} $ and $ 1 $ to get $ \dfrac{ \color{purple}{ y+8 } }{ y }$.

Step 1: Write $ 1 $ 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 $\color{blue}{y}$.

$$ \begin{aligned} \frac{8}{y} +1 & \xlongequal{\text{Step 1}} \frac{8}{y} + \frac{1}{\color{red}{1}} = \frac{ 8 }{ y } + \frac{ 1 \cdot \color{blue}{ y }}{ 1 \cdot \color{blue}{ y }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8 } }{ y } + \frac{ \color{purple}{ y } }{ y }=\frac{ \color{purple}{ y+8 } }{ y } \end{aligned} $$