$\lim_{ x \to 1 }\frac{x-1}{x^2-1}=\lim_{ x \to 1 }\frac{x-1}{\left( x-1\right)\left( x+1 \right) }\\ \lim_{ x \to 1 }\frac{1}{x+1}=\frac{1}{2}$limx→1​x2−1x−1​=limx→1​(x−1)(x+1)x−1​limx→1​x+11​=21​

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