Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.3 One-sided Limits; Continuous Functions - 14.3 Assess Your Understanding - Page 890: 41

$-\frac{2}{3}$

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: $$\lim_{x\to -1^-}\frac{x-1}{(x^2-x+1)}\\=\frac{(-1)-1}{((-1)^2-(-1)+1)}=-\frac{2}{3}$$