Multiply $5$ by $ \dfrac{x}{x} $ to get $ \dfrac{ 5x }{ x } $.

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{x}{x} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{x} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot x } \xlongequal{\text{Step 3}} \frac{ 5x }{ x } \end{aligned} $$

Subtract $6$ from $ \dfrac{5x}{x} $ to get $ \dfrac{ \color{purple}{ -x } }{ x }$.

Step 1: Write $ 6 $ 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 $\color{blue}{x}$.

$$ \begin{aligned} \frac{5x}{x} -6 & \xlongequal{\text{Step 1}} \frac{5x}{x} - \frac{6}{\color{red}{1}} = \frac{ 5x }{ x } - \frac{ 6 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x } }{ x } - \frac{ \color{purple}{ 6x } }{ x }=\frac{ \color{purple}{ -x } }{ x } \end{aligned} $$