1. The problem is to evaluate the expression $$\frac{(5 + 1)^2}{(7 - 5)^2}$$. 2. The formula involves squaring sums and differences: $$(a + b)^2 = (a + b)(a + b)$$ and $$(a - b)^2 = (a - b)(a - b)$$. 3. First, simplify inside the parentheses: $$5 + 1 = 6$$ $$7 - 5 = 2$$ 4. Now square these results: $$6^2 = 36$$ $$2^2 = 4$$ 5. Substitute back into the fraction: $$\frac{36}{4}$$ 6. Finally, divide numerator by denominator: $$36 \div 4 = 9$$ So, the value of the expression is **9**.