Answer
$(b)$ and $(d)$
Work Step by Step
The domain of a rational expression is the whole set of real numbers, excluding the numbers that make the denominator equal to zero (since division of zero is not allowed).
Here, we exclude $x$ for which the denominator is equal to zero.
To find the numbers that will make the denominator zero, set the denominator equal to zero then solve the equation:
$ x^{2}-1=0\qquad$
Add $1$ from each side of the equation to obtain:
$x^{2}=1$
Take the square root of both sides:
$\sqrt{x^2}=\pm\sqrt{1}$
$x=\pm1$
Thus, the numbers that will be excluded from the domain are $-1$ and $1$..
Hence, the answer is $(b)$ and $(d)$.