# Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 29

$-\frac{1}{2}.$

#### Work Step by Step

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

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