Divide $ \dfrac{x}{7} $ by $ 9 $ to get $ \dfrac{ x }{ 63 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x}{7} }{9} & \xlongequal{\text{Step 1}} \frac{x}{7} \cdot \frac{\color{blue}{1}}{\color{blue}{9}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ 7 \cdot 9 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 63 } \end{aligned} $$

Divide $ \dfrac{x}{63} $ by $ 4 $ to get $ \dfrac{ x }{ 252 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x}{63} }{4} & \xlongequal{\text{Step 1}} \frac{x}{63} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ 63 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 252 } \end{aligned} $$

Multiply $7$ by $ \dfrac{x}{252} $ to get $ \dfrac{ 7x }{ 252 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{x}{252} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x}{252} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x }{ 1 \cdot 252 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x }{ 252 } \end{aligned} $$