Question

when x^-1 is divided by x-1 the quotient is

Answer 1

Factor x^2 - 1

HINT: Difference of two squares \[\large (p^2 - q^2) = (p+q)(p-q)\]

Answer 2

my problem is x to the negative 1st power not x^2

Answer 3

Whoops... I'm sorry, I must have been seeing things :)
If that's the case, then.
\[\huge \frac{x^{-1}}{x-1}= x^{-1}\cdot \frac{1}{x-1}\]

and the fact that \[\huge x^{-1} = \frac1x\]