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

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 $\color{blue}{ x }$.

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

Divide $3$ by $ \dfrac{xy+5}{x} $ to get $ \dfrac{ 3x }{ xy+5 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

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