Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Chapter Review - Review Exercises - Page 906: 9

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Factor each polynomial: $$\lim_{x\to -1^-}\frac{x^2-1}{x^3-1}\\=\lim_{x\to -1^-}\frac{(x+1)(x-1)}{(x-1)(x^2+x+1)}.$$ Cancel the common factors: $$\lim_{x\to -1^-}\frac{x+1}{x^2+x+1}\\=\frac{(-1)+1}{(-1)^2+(-1)+1}\\=\frac{0}{1}=0$$