# What is the limit of ( 1/(x-1) - 2/(x^2-1) ) as x approaches 1?

${\lim}_{x \rightarrow 1} \left(\frac{1}{x - 1} - \frac{2}{{x}^{2} - 1}\right) = {\lim}_{x \rightarrow 1} \frac{\left(x + 1\right) - 2}{\left(x + 1\right) \left(x - 1\right)}$
$= {\lim}_{x \rightarrow 1} \frac{x - 1}{\left(x + 1\right) \left(x - 1\right)} = {\lim}_{x \rightarrow 1} \frac{1}{x + 1} = \frac{1}{2}$