Domain

$\frac{1}{(t-1)^2-(t+1)^2}$

Let's  simplify  the denominator   as    [ t^2 - 2t + 1 ]  - [ t^2 + 2t + 1 ]   =   -4t

Note  that we can't have  0   as the denomiator, so  the only value  that  makes 4t   =  0    is when t = 0

Then  the domain for t is   ( -infinity , 0)  U  ( 0  , infinity )