1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$ 2. **Understand the given information:** We know both $a - b$ and $b - c$ equal 2. 3. **Calculate the numerator:** $$(a - b)^2 + (b - c)^2 = 2^2 + 2^2 = 4 + 4 = 8$$ 4. **Find $a - c$:** Since $a - b = 2$ and $b - c = 2$, adding these gives: $$a - c = (a - b) + (b - c) = 2 + 2 = 4$$ 5. **Calculate the denominator:** $$(a - c)^2 = 4^2 = 16$$ 6. **Form the fraction and simplify:** $$\frac{8}{16} = \frac{\cancel{8}}{\cancel{16}} = \frac{1}{2}$$ 7. **Final answer:** $$\boxed{\frac{1}{2}}$$