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

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

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