If a - b = b - c = 2, what is the value of (a - b)^2 + (b - c)^2 / (a - c)^2?

1. Identify given information: We are given that $a - b = 2$ and $b - c = 2$. We need to find the value of the expression $\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$.

2. Determine the value of (a - c): Since $a - b = 2$ and $b - c = 2$, we can add these two equations together.
$(a - b) + (b - c) = 2 + 2$
$a - b + b - c = 4$
$a - c = 4$

3. Substitute known values into the expression: Now we have the values for $(a - b)$, $(b - c)$, and $(a - c)$. We can substitute these values into the given expression.
$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2} = \frac{(2)^2 + (2)^2}{(4)^2}$

4. Calculate the squares: Square each of the numbers in the expression.
$\frac{4 + 4}{16}$

5. Perform addition and division: Add the numbers in the numerator and then divide by the denominator.
$\frac{8}{16}$
$\frac{1}{2}$