# How do you find the domain for f(x)=(x+5)/(x^2-25)?

Aug 11, 2016

The Domain of $f$ is $\mathbb{R} - \left\{\pm 5\right\}$.

#### Explanation:

As division by Zero is not allowed, we must have, ${x}^{2} - 25 \ne 0$.

As, ${x}^{2} - 25 = 0 \Rightarrow \left(x - 5\right) \left(x + 5\right) = 0 \Rightarrow x = \pm 5$

$\therefore x 62 - 25 \ne 0 \Rightarrow x \ne \pm 5$.

Hence, the Domain of $f$ is $\mathbb{R} - \left\{\pm 5\right\}$.