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

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ x }$ and the second by $\color{blue}{ x-2 }$.

$$ \begin{aligned} \frac{x}{x-2} - \frac{3}{x} & = \frac{ x \cdot \color{blue}{ x }}{ \left( x-2 \right) \cdot \color{blue}{ x }} - \frac{ 3 \cdot \color{blue}{ \left( x-2 \right) }}{ x \cdot \color{blue}{ \left( x-2 \right) }} = \\[1ex] &=\frac{ \color{purple}{ x^2 } }{ x^2-2x } - \frac{ \color{purple}{ 3x-6 } }{ x^2-2x }=\frac{ \color{purple}{ x^2 - \left( 3x-6 \right) } }{ x^2-2x } = \\[1ex] &=\frac{ \color{purple}{ x^2-3x+6 } }{ x^2-2x } \end{aligned} $$