Add $y$ and $ \dfrac{2}{y} $ to get $ \dfrac{ \color{purple}{ y^2+2 } }{ y }$.

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

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

Subtract $5$ from $ \dfrac{y^2+2}{y} $ to get $ \dfrac{ \color{purple}{ y^2-5y+2 } }{ y }$.

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

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