Subtract $ \dfrac{p}{8} $ from $ \dfrac{x}{4} $ to get $ \dfrac{ \color{purple}{ -p+2x } }{ 8 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{x}{4} - \frac{p}{8} & = \frac{ x \cdot \color{blue}{ 2 }}{ 4 \cdot \color{blue}{ 2 }} - \frac{ p }{ 8 } = \\[1ex] &=\frac{ \color{purple}{ 2x } }{ 8 } - \frac{ \color{purple}{ p } }{ 8 }=\frac{ \color{purple}{ -p+2x } }{ 8 } \end{aligned} $$

Divide $ \dfrac{-p+2x}{8} $ by $ p $ to get $ \dfrac{ -p+2x }{ 8p } $.

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.

$$ \begin{aligned} \frac{ \frac{-p+2x}{8} }{p} & \xlongequal{\text{Step 1}} \frac{-p+2x}{8} \cdot \frac{\color{blue}{1}}{\color{blue}{p}} \xlongequal{\text{Step 2}} \frac{ \left( -p+2x \right) \cdot 1 }{ 8 \cdot p } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -p+2x }{ 8p } \end{aligned} $$