Answer
$(-∞,-1)∪(-1,1)∪(1,∞)$
Work Step by Step
Making $x=−1,1$ results in an undefined function, so those values are excluded from the domain.
$g(x)=\frac{1}{x^2+1}-\frac{1}{x^2-1}$
$g(x)=\frac{1}{x^2+1}-\frac{1}{(x+1)(x-1)}$
$(-∞,-1)∪(-1,1)∪(1,∞)$
