# How do you simplify and state the excluded values for (x+5) /(x^2-25)?

May 26, 2015

Note that $\frac{x + 5}{{x}^{2} - 25}$ is only defined if the denominator is not equal to zero.
That is ${x}^{2} - 25 \ne 0$
$\rightarrow x = 5$ and $x = - 5$ are excluded values.

If $x \ne \pm 5$
then
$\frac{x + 5}{{x}^{2} - 25}$

$= \frac{x + 5}{\left(x + 5\right) \left(x - 5\right)}$

$= \frac{\cancel{x + 5}}{\cancel{x + 5} \left(x - 5\right)}$

$= \frac{1}{x - 5}$