Answer
$-\frac{1}{2}.$
Work Step by Step
We have
$$
\lim _{x \rightarrow 1}\left(\frac{1}{1-x}-\frac{2}{1-x^{2}}\right)=\lim _{x \rightarrow 1} \frac{1-x^{2}-2+2x}{(1-x)(1-x^{2})} \\
=\lim _{x \rightarrow 1} \frac{ -(x^{2}-2x+1)}{(1-x)(1-x^{2})} =\lim _{x \rightarrow 1} \frac{ -(x-1)^2}{(1-x)(1-x )(1+x)} =-\frac{1}{2}.
$$
