Multiply $ \dfrac{m}{m} $ by $ 2 $ to get $ \dfrac{ 2m }{ m } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{m}{m} \cdot 2 & \xlongequal{\text{Step 1}} \frac{m}{m} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ m \cdot 2 }{ m \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 2m }{ m } \end{aligned} $$

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

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 $\color{blue}{m}$.

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