1. **State the problem:** We are given the function $F(x) = 1 + \frac{1}{x^2} + 1$ and need to simplify it. 2. **Combine like terms:** Notice that $1 + 1 = 2$, so the function becomes: $$F(x) = 2 + \frac{1}{x^2}$$ 3. **Final simplified form:** The function is now: $$F(x) = 2 + \frac{1}{x^2}$$ This is the simplest form of the given function. **Answer:** $F(x) = 2 + \frac{1}{x^2}$