Answer
$-\dfrac{1}{2}$
Work Step by Step
L'Hospital's rule states that $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{A'(x)}{B'(x)}$
Here, $\lim\limits_{x \to 1} f(0)=\dfrac{0}{0}$
This shows an indeterminate form of the limit, so we need to use L'Hospital's rule.
$\lim\limits_{x \to 1} \dfrac{-1+1/x)}{1-(1/x)+\ln x}=\dfrac{0}{0}$
This shows an indeterminate form of the limit, so we need to use L'Hospital's rule.
$\lim\limits_{x \to 1} \dfrac{-1/x^2}{1+x/x^2}=-\dfrac{1}{1+1}=-\dfrac{1}{2}$
