The expression you've given is:

\[
\frac{x^2 - 5x - 14}{x^2 + 4x + 14}
\]

Let's simplify this expression by first analyzing both the numerator and denominator:

### Numerator: \(x^2 - 5x - 14\)
The quadratic expression doesn't factor nicely into integers, so we'll leave it as is for now.

### Denominator: \(x^2 + 4x + 14\)
Similarly, this quadratic doesn't factor easily into integers.

Since neither the numerator nor the denominator can be factored simply, the expression cannot be simplified further in terms of common factors. The expression remains:

\[
\frac{x^2 - 5x - 14}{x^2 + 4x + 14}
\]

However, you can evaluate this expression for specific values of \(x\), or use it as is in further operations.

Would you like any further details on this, or help with anything else?

### Related questions:
1. How do you factor quadratics when possible?
2. What methods are used to simplify rational expressions?
3. How can you evaluate this expression for specific values of \(x\)?
4. What are the conditions under which a quadratic can be factored?
5. How can graphing help in understanding the behavior of this rational function?

**Tip:** Always check for common factors in both the numerator and denominator when simplifying rational expressions.

Learn how to simplify the rational expression (x² - 5x - 14) / (x² + 4x + 14) by analyzing the quadratic terms in the numerator and denominator. This algebra problem explores factoring and simplification techniques suitable for students in Grades 9-11.

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