To find the x-intercepts of the function:

$y = \frac{x - 5}{x^2 - 1}$

we set $y = 0$ and solve for $x$, because the x-intercept occurs where $y = 0$.

Step 1: Set the function equal to zero

$0 = \frac{x - 5}{x^2 - 1}$

Step 2: Solve the equation

The only way for a fraction to be zero is for the numerator to be zero (the denominator must not be zero).

$x - 5 = 0$

So,

$x = 5$

Step 3: Check the denominator

We also need to check when the denominator is zero, because those values are undefined points (asymptotes) on the graph and cannot be x-intercepts.

Set $x^2 - 1 = 0$:

$x^2 = 1$

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

So, the function is undefined at $x = 1$ and $x = -1$, meaning these cannot be x-intercepts.

Final Answer:

The only x-intercept is $x = 5$.

Thus, the correct answer is B) 5.

Would you like more details or have any further questions?

Here are five related questions:

1. How do you find the y-intercepts of a rational function?
2. What happens when both the numerator and the denominator are zero at the same point?
3. How do vertical asymptotes affect the graph of a rational function?
4. Can a function have more than one x-intercept? Explain why.
5. What are horizontal asymptotes, and how do they relate to rational functions?

Tip: Always check for undefined points in rational functions by analyzing the denominator, as these indicate vertical asymptotes.