1. The problem is to find the expression for $\arctan\left(\frac{1}{x^2-1}\right)$.\n\n2. Recall that $\arctan(y)$ is the inverse tangent function, which gives the angle whose tangent is $y$.\n\n3. Here, the argument of $\arctan$ is $\frac{1}{x^2-1}$. This expression is defined for all $x$ such that $x^2-1 \neq 0$, i.e., $x \neq \pm 1$.\n\n4. There is no further simplification possible for $\arctan\left(\frac{1}{x^2-1}\right)$ without additional context or constraints.\n\n5. Therefore, the expression remains as $\arctan\left(\frac{1}{x^2-1}\right)$, which can be evaluated for specific values of $x$ avoiding $\pm 1$.