Answer
Several errors were made. See below.
The correct answer is: $-\infty$
Work Step by Step
First of all, a form $\displaystyle \frac{0}{0}$ is indeterminate, which means "can not be directly determined". It could be 0, but it could be not.
Secondly, the form is not $\displaystyle \frac{0}{0}$, but $\displaystyle \frac{1}{-0},$ which veers off toward $-\infty$, as will be shown below.
Some algebraic manipulation was overseen.
The denominator is a square of a binomial, and the common term cancels.
$\displaystyle \lim_{x\rightarrow 1^{- }}\frac{(x-1)}{(x-1)^{2}}=\lim_{x\rightarrow 1^{- }}\frac{1}{x-1}$
The denominator is a small negative number. We have
$\displaystyle \frac{1}{-0}$
$=-\infty$
