It looks like you are providing a mathematical function, but the notation is a bit unclear. Let me clarify the function based on your input.

You wrote:  
\[ f(X) = \frac{x}{\chi^2 - x - 6} \]

However, it's unclear if you meant \(\chi^2\) (the chi-squared symbol), \(x^2\), or something else. To clarify:

1. If you meant \(\chi^2\), then the function is:
   \[ f(x) = \frac{x}{\chi^2 - x - 6} \]
   where \(\chi^2\) is a constant.

2. If you meant \(x^2\), then the function is:
   \[ f(x) = \frac{x}{x^2 - x - 6} \]

Can you confirm which one you meant, or provide any additional details? If it is the second option, we can proceed with analyzing the function further, such as finding its domain, intercepts, asymptotes, or other properties.

### Questions You Might Find Helpful:
1. Would you like me to simplify or factor the expression in the denominator?
2. Are you interested in finding the domain of the function?
3. Would you like to determine any vertical or horizontal asymptotes?
4. Are you looking for the roots or intercepts of the function?
5. Should we discuss the behavior of the function for large or small values of \(x\)?

**Tip:** When writing functions, use parentheses to clarify the order of operations and ensure the expression is correctly interpreted.

Understand the function f(x) = x / (x^2 - x - 6) with a breakdown of its rational form, asymptotes, and factoring of the quadratic expression. Suitable for high school students studying algebra and rational functions.

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