A rational expression of the form
[tex]r(x)= \dfrac{p(x)}{q(x)} [/tex]
will be undefined for the zeros of the expression [tex]q(x)[/tex]. For an expression with a zero equal to 1, the simplest way is to use [tex](x-1)[/tex] as a factor in [tex]q(x)[/tex]. In can be your only one, or you can mix in other factors.
But, so long as the denominator of [tex]r(x)[/tex] is equal to zero, as it is when [tex]q(x)=x-1[/tex], the expression will be undefined at that point x, because it would involve division by zero.
You could use as your sample:
[tex] \dfrac{x-7}{x-1} [/tex]
You can try to get fancy and square some factors or add in some radicals or trigonometric functions or anything else, so long as the 1 makes the denominator equal to zero!
