https://file.aiquickdraw.com/mathbot/file/1729229031366sp5fjbtu.jpg

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.

What are the x-intercept(s) of the function y = (x - 5) / (x^2 - 1)?

Learn how to find the x-intercepts of the function y = (x - 5) / (x^2 - 1). This problem explores key algebraic concepts such as solving rational equations and identifying undefined points, suitable for students in Grades 9-11.

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