To find the vertical asymptotes for the equation $y = \frac{x + 4}{x^2 - 1}$, we need to identify the values of $x$ that make the denominator equal to zero, since division by zero is undefined and typically indicates a vertical asymptote.

Step 1: Set the denominator equal to zero.

$x^2 - 1 = 0$

Step 2: Solve for $x$.

This is a difference of squares, which can be factored as: $(x - 1)(x + 1) = 0$ Thus, $x - 1 = 0$ or $x + 1 = 0$.

Step 3: Find the values of $x$.

$x = 1 \quad \text{or} \quad x = -1$

Conclusion:

The vertical asymptotes occur at $x = 1$ and $x = -1$.

Would you like more details on this solution or have any other questions?

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Here are five related questions to expand your understanding:

1. How do you find the horizontal asymptotes of a rational function?
2. What is the behavior of the function as it approaches the vertical asymptotes?
3. How can you find the slant (oblique) asymptotes of a rational function?
4. How does the presence of vertical asymptotes affect the graph of the function?
5. Can a function have more than two vertical asymptotes?

Tip: Always remember to check for holes in the graph of a rational function, which occur when both the numerator and denominator have a common factor that can be canceled out.