1. The problem asks to evaluate the expressions $\frac{4.12 + 6.71}{8.76 - 8.76}$ and $\frac{0.13 - 0.13}{100 - 100}$. 2. The formula used is division of sums and differences: $\frac{a + b}{c - d}$ or $\frac{a - b}{c - d}$. 3. Calculate the numerator and denominator for the first expression: $$4.12 + 6.71 = 10.83$$ $$8.76 - 8.76 = 0$$ 4. The first expression becomes: $$\frac{10.83}{0}$$ 5. Division by zero is undefined in mathematics, so the first expression is undefined. 6. Calculate the numerator and denominator for the second expression: $$0.13 - 0.13 = 0$$ $$100 - 100 = 0$$ 7. The second expression becomes: $$\frac{0}{0}$$ 8. The form $\frac{0}{0}$ is indeterminate, meaning it does not have a defined value without further context. 9. Therefore, both expressions involve division by zero, which is not allowed, making them undefined or indeterminate.