To simplify the expression \(\frac{x^2 + 6x - 16}{2 - x}\), follow these steps:

1. **Factor the numerator**: We need to factor the quadratic expression \(x^2 + 6x - 16\).
   - Look for two numbers that multiply to \(-16\) and add to \(6\). The numbers \(8\) and \(-2\) work because \(8 \times (-2) = -16\) and \(8 + (-2) = 6\).
   - So, \(x^2 + 6x - 16\) factors as \((x + 8)(x - 2)\).

   Therefore:
   \[
   \frac{x^2 + 6x - 16}{2 - x} = \frac{(x + 8)(x - 2)}{2 - x}
   \]

2. **Simplify the expression**: Notice that \(x - 2\) and \(2 - x\) are related. Specifically, \(2 - x\) is \(-(x - 2)\).
   \[
   \frac{(x + 8)(x - 2)}{-(x - 2)} = -\frac{(x + 8)(x - 2)}{x - 2}
   \]

3. **Cancel out the common factor**: The \(x - 2\) in the numerator and denominator cancels out, leaving:
   \[
   -(x + 8)
   \]

4. **Final answer**: 
   \[
   -(x + 8) = -x - 8
   \]

So, \(\frac{x^2 + 6x - 16}{2 - x} = -x - 8\), assuming \(x \neq 2\) (since \(x = 2\) would make the denominator zero, which is undefined).

Would you like to explore more details, or do you have any questions?

Here are some related questions:
1. How does factoring quadratics help in simplifying rational expressions?
2. What happens if the denominator is a more complex expression?
3. How do you determine when two expressions are equivalent?
4. Can you graph \(-x - 8\) to see its behavior?
5. What are the consequences if \(x = 2\) in this expression?

**Tip:** Always check for any restrictions on the variable after simplifying an expression, especially when canceling factors.

Simplify the expression (x^2 + 6x - 16) / (2 - x).

Explore the step-by-step solution to simplifying the rational expression (x^2 + 6x - 16) / (2 - x). This problem delves into algebraic concepts like factoring and the relationship between similar expressions, tailored for students in Grades 9-10.

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