1. **State the problem:** Simplify the expression $\frac{\sqrt{1}}{4 - x^2}$. 2. **Recall the properties:** The square root of 1 is 1 because $\sqrt{1} = 1$. 3. **Simplify the numerator:** $\sqrt{1} = 1$. 4. **Rewrite the denominator:** $4 - x^2$ is a difference of squares and can be factored as $(2 - x)(2 + x)$. 5. **Final simplified form:** $$\frac{1}{(2 - x)(2 + x)}$$ This is the simplified expression.