Divide $ \dfrac{x+5}{4} $ by $ x^2+5x $ to get $ \dfrac{ 1 }{ 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.

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