Answer
$\mathrm{Neither\:even\:nor\:odd}.$
Work Step by Step
$\mathrm{Function\:Parity\:Definition:} $
$\mathrm{Even\:Function:}\:\: $ A function is even if $\ h(-t)=h(t)\ $ for all $\ x\in \mathbb{R}. $
$\mathrm{Odd\:Function:}\:\: $ A function is odd if $\ h(-t)=-h(t)\ $ for all $\ x\in \mathbb{R}. $
$h(t)=\frac{1}{t-1}$
$h(-t)=\frac{1}{-t-1}$
Now,
$-h(t)=-\frac{1}{t-1}$
Since,
$h(-t)\ne h(t)\mathrm{,\:therefore\:}\frac{1}{t-1}\mathrm{\:is\:not\:an\:even\:function}$
$h(-t)\ne -h(t)\mathrm{,\:therefore\:}\frac{1}{t-1}\mathrm{\:is\:not\:an\:odd\:function}$
