Which of the following cannot be a value of 1/x-1?

I don't get the explanation for this problem. The OG says "since 1 divided by any number can never equal zero".
if x=0 then the value would be 1/-1=-1.

Am I missing something?

thanks!

Please post the complete text of the problem, including answer choices. Please also make sure to use parentheses or other formatting when necessary - for instance, should this problem read 1/(x-1) or (1/x) - 1? Thanks!

Please also clarify your question - the OG says the outcome of the division can't equal zero and the example you gave does not, in fact, equal zero. It equals -1. You set x=0, but the excerpt you quoted from OG does not say x can't equal zero.