Answer
$\mathrm{Even}.$
Work Step by Step
$\mathrm{Function\:Parity\:Definition:} $
$\mathrm{Even\:Function:}\:\: $ A function is even if $\ g(-x)=g(x)\ $ for all $\ x\in \mathbb{R}. $
$\mathrm{Odd\:Function:}\:\: $ A function is odd if $\ g(-x)=-g(x)\ $ for all $\ x\in \mathbb{R}. $
$g(x)=\frac{1}{x^2-1}$
$g(-x)=\frac{1}{(-x)^2-1}$
$g(-x)=\frac{1}{x^2-1}$
Now,
$-g(x)=-\frac{1}{x^2-1}$
Since,
$g(-x)=g(x)\mathrm{,\:therefore\:}\frac{1}{x^2-1}\mathrm{\:is\:an\:even\:function}$
$g(-x)\ne-g(x)\mathrm{,\:therefore\:}\frac{1}{x^2-1}\mathrm{\:is\:not\:an\:odd\:function}$
