Subtract $1$ from $ \dfrac{x}{7} $ to get $ \dfrac{ \color{purple}{ x-7 } }{ 7 }$.

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 second fraction by $\color{blue}{7}$.

$$ \begin{aligned} \frac{x}{7} -1 & \xlongequal{\text{Step 1}} \frac{x}{7} - \frac{1}{\color{red}{1}} = \frac{ x }{ 7 } - \frac{ 1 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x } }{ 7 } - \frac{ \color{purple}{ 7 } }{ 7 }=\frac{ \color{purple}{ x-7 } }{ 7 } \end{aligned} $$

Divide $ \dfrac{x-7}{7} $ by $ x-7 $ to get $ \dfrac{1}{7} $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Cancel $ \color{blue}{ x-7 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

$$ \begin{aligned} \frac{ \frac{x-7}{7} }{x-7} & \xlongequal{\text{Step 1}} \frac{x-7}{7} \cdot \frac{\color{blue}{1}}{\color{blue}{x-7}} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{7} \cdot \frac{1}{\color{blue}{1}} = \\[1ex] &= \frac{1}{7} \end{aligned} $$