The given function is:

\[
f(x) = \frac{4 - 3x - x^2}{x^2 - 1}
\]

Let's break it down:

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

2. **Rearrange the numerator**:  
   The numerator \( 4 - 3x - x^2 \) can be rewritten in a more familiar form:
   \[
   4 - 3x - x^2 = -x^2 - 3x + 4
   \]

Thus, the function becomes:

\[
f(x) = \frac{-x^2 - 3x + 4}{(x - 1)(x + 1)}
\]

This is the simplified form of the function. If you'd like, I can help you analyze the function further (e.g., finding intercepts, asymptotes, or limits). Would you like to go into more details?

Here are some related questions:
1. How do you find the vertical asymptotes of a rational function?
2. How can we factor the numerator further to simplify \( f(x) \)?
3. What is the domain of this rational function?
4. How can we find the intercepts of this function?
5. What is the end behavior of the function as \( x \to \infty \)?

**Tip**: Always check if both the numerator and denominator can be factored when simplifying rational functions.

Learn how to simplify the rational function f(x) = (4 - 3x - x²) / (x² - 1) by factoring the denominator and rearranging the numerator. This problem covers key algebraic concepts like rational expressions, factoring techniques, and more. Suitable for students in Grades 9-12.

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