1. **State the problem:** Simplify the fraction $$\frac{x - a}{a - x}$$. 2. **Recognize the relationship:** Notice that the denominator $$a - x$$ can be rewritten as $$-(x - a)$$ because $$a - x = -(x - a)$$. 3. **Rewrite the fraction:** Substitute the denominator: $$\frac{x - a}{a - x} = \frac{x - a}{-(x - a)}$$ 4. **Simplify by canceling common factors:** Since $$x - a$$ appears in both numerator and denominator, we can cancel it out: $$\frac{\cancel{x - a}}{-\cancel{x - a}} = -1$$ 5. **Final answer:** The simplified form of the fraction is $$-1$$. This means the original fraction always equals $$-1$$ for all values of $$x$$ and $$a$$ where the denominator is not zero (i.e., $$x \neq a$$).