Question

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

Answer 1

Note that `(x+5)/(x^2-25)` is only defined if the denominator is not equal to zero.
That is `x^2-25 != 0`
`rarr x=5` and `x=-5` are excluded values.

If `x!=+-5`
then
`(x+5)/(x^2-25)`

`= (x+5)/((x+5)(x-5))`

`= cancel(x+5)/(cancel(x+5)(x-5))`

`= 1/(x-5)`