Answer
$(-∞,-2)∪(-2,2)∪(2,∞)$
Work Step by Step
Making $x=−2,2$ results in an undefined function, so those values are excluded from the domain.
$g(x)=\frac{1}{x^2+4}-\frac{1}{x^2-4}$
$g(x)=\frac{1}{x^2+4}-\frac{1}{(x+2)(x-2)}$
$(-∞,-2)∪(-2,2)∪(2,∞)$
