https://file.aiquickdraw.com/mathbot/file/1726982939772xu03r5re.jpg

The expression in the image is:

\[
\frac{x^2 - x - 14}{x^2 - 2x - 3}
\]

### Step 1: Factor both the numerator and denominator.

#### Numerator: \( x^2 - x - 14 \)
We need to factor this quadratic expression. However, after attempting to factor, it seems this quadratic does not factor nicely into integers. Thus, we leave the numerator as is for now:

\[
x^2 - x - 14
\]

#### Denominator: \( x^2 - 2x - 3 \)
This quadratic can be factored using simple factoring methods:

\[
x^2 - 2x - 3 = (x - 3)(x + 1)
\]

### Step 2: Rewrite the expression

Now we write the fraction with the factored denominator:

\[
\frac{x^2 - x - 14}{(x - 3)(x + 1)}
\]

Since the numerator does not factor neatly, the fraction cannot be simplified further without knowing more about the domain or specific values of \(x\).

Would you like more details on any of the steps or help solving related problems? Here are a few questions you could explore next:

1. How do you factor quadratic expressions that don't factor easily into integers?
2. What is the process for simplifying complex rational expressions?
3. How would you find the domain of this rational expression?
4. How can you use the quadratic formula to find the roots of the numerator \(x^2 - x - 14\)?
5. How can this expression be evaluated for specific values of \(x\)?

### Tip: 
When factoring quadratics, always check if the discriminant (the part under the square root in the quadratic formula) suggests that the quadratic can factor over the integers.

Simplify the rational expression \( \frac{x^2 - x - 14}{x^2 - 2x - 3} \).

Learn how to simplify the rational expression \( \frac{x^2 - x - 14}{x^2 - 2x - 3} \) by factoring the denominator and attempting to factor the numerator. This step-by-step guide covers factoring quadratics and simplifying rational expressions, suitable for Grades 9-12.

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