Subtract $ \dfrac{7}{8x-20} $ from $ \dfrac{1}{2x-5} $ to get $ \dfrac{ \color{purple}{ -3 } }{ 8x-20 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{1}{2x-5} - \frac{7}{8x-20} & = \frac{ 1 \cdot \color{blue}{ 4 }}{ \left( 2x-5 \right) \cdot \color{blue}{ 4 }} - \frac{ 7 }{ 8x-20 } = \\[1ex] &=\frac{ \color{purple}{ 4 } }{ 8x-20 } - \frac{ \color{purple}{ 7 } }{ 8x-20 }=\frac{ \color{purple}{ -3 } }{ 8x-20 } \end{aligned} $$

Divide $ \dfrac{-3}{8x-20} $ by $ \dfrac{x}{2x-5} $ to get $ \dfrac{ -3 }{ 4x } $.

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

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

Step 5: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{-3}{8x-20} }{ \frac{\color{blue}{x}}{\color{blue}{2x-5}} } & \xlongequal{\text{Step 1}} \frac{-3}{8x-20} \cdot \frac{\color{blue}{2x-5}}{\color{blue}{x}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -3 }{ 4 \cdot \color{red}{ \left( 2x-5 \right) } } \cdot \frac{ 1 \cdot \color{red}{ \left( 2x-5 \right) } }{ x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -3 }{ 4 } \cdot \frac{ 1 }{ x } \xlongequal{\text{Step 4}} \frac{ \left( -3 \right) \cdot 1 }{ 4 \cdot x } \xlongequal{\text{Step 5}} \frac{ -3 }{ 4x } \end{aligned} $$