1. State the problem: If $a - b = b - c = 2$, what is the value of the expression $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. Formula and rules: Use the identity $a - c = (a - b) + (b - c)$ and perform substitution and algebraic simplification. 3. Substitute known values: Since $a - b = 2$ and $b - c = 2$, compute numerator and denominator. Numerator: $(a - b)^2 + (b - c)^2 = 2^2 + 2^2 = 4 + 4 = 8$. Denominator: $a - c = (a - b) + (b - c) = 2 + 2 = 4$. Denominator squared: $(a - c)^2 = 4^2 = 16$. 4. Form the fraction: $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2} = \frac{8}{16}$$. 5. Simplify by canceling common factors: $$\frac{8}{16} = \frac{\cancel{8}}{\cancel{16}} = \frac{1}{2}$$. 6. Final answer: The value is $\frac{1}{2}$.