1. **State the problem:** Simplify the expression $$\frac{x+1}{x-4} - \frac{x+4}{5x-20}$$. 2. **Identify the denominators:** The denominators are $x-4$ and $5x-20$. 3. **Factor the second denominator:** $$5x-20 = 5(x-4)$$ 4. **Find the common denominator:** The least common denominator (LCD) is $$5(x-4)$$. 5. **Rewrite each fraction with the LCD:** $$\frac{x+1}{x-4} = \frac{5(x+1)}{5(x-4)}$$ $$\frac{x+4}{5(x-4)}$$ stays the same. 6. **Rewrite the expression:** $$\frac{5(x+1)}{5(x-4)} - \frac{x+4}{5(x-4)} = \frac{5(x+1) - (x+4)}{5(x-4)}$$ 7. **Simplify the numerator:** $$5(x+1) - (x+4) = 5x + 5 - x - 4 = (5x - x) + (5 - 4) = 4x + 1$$ 8. **Final simplified expression:** $$\frac{4x + 1}{5(x-4)}$$ **Answer:** $$\frac{4x + 1}{5(x-4)}$$