1. **State the problem:** Simplify the expression $$\frac{8}{1-2x} + \frac{x}{2x-1}$$. 2. **Identify the denominators:** The denominators are $$1-2x$$ and $$2x-1$$. 3. **Note the relationship between denominators:** $$2x-1 = -(1-2x)$$ because $$2x-1 = -1(1-2x)$$. 4. **Rewrite the second fraction:** $$\frac{x}{2x-1} = \frac{x}{-(1-2x)} = -\frac{x}{1-2x}$$. 5. **Combine the fractions:** $$\frac{8}{1-2x} + \left(-\frac{x}{1-2x}\right) = \frac{8 - x}{1-2x}$$. 6. **Final simplified expression:** $$\boxed{\frac{8 - x}{1-2x}}$$. This is the simplified form of the original expression.