Answer
$\lim\limits_{x \to 1}\frac{x^{-1}-1}{(x-1)} = -1$
Work Step by Step
Simplify:
$\frac{x^{-1}-1}{(x-1)} = \frac{(1-x)}{x(x-1)} = -\frac{(x-1)}{x(x-1)} = -\frac{1}{x}$
Now,
$\lim\limits_{x \to 1}\frac{x^{-1}-1}{(x-1)} = -\lim\limits_{x \to 1}\frac{1}{x} = -1$
