Let's solve this step by step! 🎉 **Step 1:** We are told $a - b = 2$ and $b - c = 2$. **Step 2:** Let's find $a - c$ using these: $$a - c = (a - b) + (b - c) = 2 + 2 = 4$$ **Step 3:** Now, look at the fraction: $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$ **Step 4:** Substitute values: $$\frac{2^2 + 2^2}{4^2} = \frac{4 + 4}{16} = \frac{8}{16}$$ **Step 5:** Simplify: $$\frac{8}{16} = \frac{1}{2}$$ Great job! The answer is $\frac{1}{2}$. Imagine you have two groups of 2 apples each 🍎🍎 and 🍎🍎, and together 4 apples 🍎🍎🍎🍎. We are comparing the squares of small groups to the big group squared. Cool! 🎯