1. **State the problem:** Simplify the expression $\frac{X}{2x^2 - 1}$. 2. **Identify the expression:** The numerator is $X$ and the denominator is $2x^2 - 1$. 3. **Check for common factors:** There are no common factors between $X$ and $2x^2 - 1$ since $X$ is a variable and $2x^2 - 1$ is a quadratic expression. 4. **Conclusion:** The expression is already in its simplest form because the numerator and denominator share no common factors. **Final answer:** $$\frac{X}{2x^2 - 1}$$