Subtract $9x$ from $ \dfrac{5}{2x} $ to get $ \dfrac{ \color{purple}{ -18x^2+5 } }{ 2x }$.

Step 1: Write $ 9x $ 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 $\color{blue}{2x}$.

$$ \begin{aligned} \frac{5}{2x} -9x & \xlongequal{\text{Step 1}} \frac{5}{2x} - \frac{9x}{\color{red}{1}} = \frac{ 5 }{ 2x } - \frac{ 9x \cdot \color{blue}{ 2x }}{ 1 \cdot \color{blue}{ 2x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5 } }{ 2x } - \frac{ \color{purple}{ 18x^2 } }{ 2x }=\frac{ \color{purple}{ -18x^2+5 } }{ 2x } \end{aligned} $$