Answer
$\text{odd}$
Work Step by Step
Recall:
a) A function is said to be odd, when every number $x$ in its domain, the number $-x$ is also in the domain such that $h(-x)=-h(x)$
b) A function is said to be even, when every number $x$ in its domain, the number $-x$ is also in the domain such that $h(-x)=h(x)$
Replace $x$ with $-x$ to evaluate $h(-x)$:
$h(-x)=\dfrac{-x}{(-x)^2-1} \\=-\dfrac{x}{x^2-1} \\=-h(x)$
Therefore, the function $h(x)$ is odd.
