Enter the simplified form of the expression x²+4x-12/2x+12

To simplify the expression \(\frac{x^2 + 4x - 12}{2x + 12}\), follow these steps:

1. **Factor the numerator and denominator**:

   - **Numerator**: \(x^2 + 4x - 12\)  
     Factor \(x^2 + 4x - 12\). Find two numbers that multiply to \(-12\) and add to \(4\). These numbers are \(6\) and \(-2\), so:
     \[
     x^2 + 4x - 12 = (x + 6)(x - 2)
     \]

   - **Denominator**: \(2x + 12\)  
     Factor out the greatest common factor (GCF), which is \(2\):
     \[
     2x + 12 = 2(x + 6)
     \]

2. **Simplify** the expression:
   \[
   \frac{(x + 6)(x - 2)}{2(x + 6)}
   \]
   Since \(x + 6\) is common in both the numerator and the denominator, cancel it out:
   \[
   \frac{x - 2}{2}
   \]

So, the simplified form of the expression is:

\[
\frac{x - 2}{2}
\]

Would you like further clarification or more details on any step?

Here are some related questions to expand on this concept:

1. How do you factor quadratic expressions like \(x^2 + 4x - 12\)?
2. What is the greatest common factor (GCF) and how is it used in factoring?
3. How do you cancel terms when simplifying fractions?
4. What are the conditions for a rational expression to be undefined?
5. Can we simplify a fraction when the numerator and denominator contain terms that cannot be factored?

**Tip**: Always check for common factors before simplifying fractions.

Enter the simplified form of the expression x² + 4x - 12 / 2x + 12.

Learn how to simplify the rational expression x² + 4x - 12 / 2x + 12 using factoring and common factor cancellation. This step-by-step guide covers factoring quadratic expressions and simplifying rational fractions, suitable for students in Grades 9-11.

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