1. **State the problem:** Simplify the expression $$\frac{4 - 3}{5x - 10} \times (x - 2)$$. 2. **Simplify the numerator:** Calculate $4 - 3$. $$4 - 3 = 1$$ 3. **Rewrite the expression:** $$\frac{1}{5x - 10} \times (x - 2)$$ 4. **Factor the denominator:** Notice that $5x - 10$ can be factored as: $$5x - 10 = 5(x - 2)$$ 5. **Substitute the factorization:** $$\frac{1}{5(x - 2)} \times (x - 2)$$ 6. **Cancel common factors:** The $(x - 2)$ terms cancel out: $$\frac{1}{5\cancel{(x - 2)}} \times \cancel{(x - 2)} = \frac{1}{5}$$ 7. **Final answer:** $$\boxed{\frac{1}{5}}$$ This means the original expression simplifies to $\frac{1}{5}$ regardless of $x$ (except where $x=2$ which would make the denominator zero).