Answer
$\{x | x \neq-5, x \neq 5\}$
Work Step by Step
$\begin{aligned} f(x) &=\frac{x^{2}-1}{x^{2}-25} \\ \text { To find the Domain } & \\ x^{2}-25 & \neq 0 \end{aligned}$
$(x+5)(x-5) \neq 0$
$(x+5) \neq 0, \quad(x-5) \neq 0$
$x \neq-5, x \neq 5$
Function is defined on all real numbers except $5 \text{ and } -5$.
$\begin{aligned} \text { Domain } &=\{x | x \neq-5, x \neq 5\} \end{aligned}$
