Add $ \dfrac{5}{2x} $ and $ \dfrac{3}{x^2} $ to get $ \dfrac{ \color{purple}{ 5x^2+6x } }{ 2x^3 }$.

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^2 }$ and the second by $\color{blue}{ 2x }$.

$$ \begin{aligned} \frac{5}{2x} + \frac{3}{x^2} & = \frac{ 5 \cdot \color{blue}{ x^2 }}{ 2x \cdot \color{blue}{ x^2 }} + \frac{ 3 \cdot \color{blue}{ 2x }}{ x^2 \cdot \color{blue}{ 2x }} = \\[1ex] &=\frac{ \color{purple}{ 5x^2 } }{ 2x^3 } + \frac{ \color{purple}{ 6x } }{ 2x^3 }=\frac{ \color{purple}{ 5x^2+6x } }{ 2x^3 } \end{aligned} $$