The expression ...
... (x+1)/(x²+2x-24)
will have a zero denominator when
... x² +2x -24 = 0
... (x +6)(x -4) = 0 . . . . . factored form
... x = -6, x = 4 . . . . . . . values of x that make the factors zero
The rational expression will be undefined when x = -6 or x = 4.
