Subtract $3x$ from $ \dfrac{1}{2x^2} $ to get $ \dfrac{ \color{purple}{ -6x^3+1 } }{ 2x^2 }$.

Step 1: Write $ 3x $ 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 $\color{blue}{2x^2}$.

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