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

Step 1: Write $ 2 $ 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 $\color{blue}{x}$.

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

Add $ \dfrac{-x}{x} $ and $ \dfrac{3}{x} $ to get $ \dfrac{ -x + 3 }{ \color{blue}{ x }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-x}{x} + \frac{3}{x} & = \frac{-x}{\color{blue}{x}} + \frac{3}{\color{blue}{x}} =\frac{ -x + 3 }{ \color{blue}{ x }} \end{aligned} $$

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

Step 1: Write $ 2 $ 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 $\color{blue}{x}$.

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