Add $ \dfrac{7}{x} $ and $ \dfrac{3}{y} $ to get $ \dfrac{ \color{purple}{ 3x+7y } }{ xy }$.

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 }$ and the second by $\color{blue}{ x }$.

$$ \begin{aligned} \frac{7}{x} + \frac{3}{y} & = \frac{ 7 \cdot \color{blue}{ y }}{ x \cdot \color{blue}{ y }} + \frac{ 3 \cdot \color{blue}{ x }}{ y \cdot \color{blue}{ x }} = \\[1ex] &=\frac{ \color{purple}{ 7y } }{ xy } + \frac{ \color{purple}{ 3x } }{ xy }=\frac{ \color{purple}{ 3x+7y } }{ xy } \end{aligned} $$