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

Step 1: Write $ 1 $ 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 first fraction by $\color{blue}{ x }$.

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

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

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^2 }$ and the second by $\color{blue}{ x }$.

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