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The given limit is:

\[
\lim_{x \to -1} \frac{x^3 + 1}{x^2 - 1}
\]

### Step-by-Step Solution:

1. **Factor the expressions**:
   - The denominator \( x^2 - 1 \) is a difference of squares, so it can be factored as:
     \[
     x^2 - 1 = (x - 1)(x + 1)
     \]
   - The numerator \( x^3 + 1 \) is a sum of cubes, and it can be factored as:
     \[
     x^3 + 1

lim (x^3 + 1) / (x^2 - 1) as x approaches -1

Solve the limit lim (x^3 + 1) / (x^2 - 1) as x approaches -1. This problem involves factoring both the numerator and the denominator using the sum of cubes and difference of squares formulas. Detailed step-by-step solution for high school students in Grades 11-12.

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