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

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

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