1. **State the problem:** Solve the equation $$\frac{2h^2 - 1}{h^2 + 1} = 0$$ for the variable $h$. 2. **Recall the rule for fractions:** A fraction equals zero if and only if its numerator is zero and the denominator is not zero. 3. **Apply the rule:** Set the numerator equal to zero: $$2h^2 - 1 = 0$$ 4. **Solve for $h^2$:** $$2h^2 = 1$$ $$h^2 = \frac{1}{2}$$ 5. **Find $h$ by taking the square root:** $$h = \pm \sqrt{\frac{1}{2}} = \pm \frac{\sqrt{2}}{2}$$ 6. **Check the denominator:** $$h^2 + 1 = \frac{1}{2} + 1 = \frac{3}{2} \neq 0$$ So the denominator is not zero, which is valid. **Final answer:** $$h = \pm \frac{\sqrt{2}}{2}$$