https://file.aiquickdraw.com/mathbot/file/1726016456998gwzpu0p5.jpg

From the image you provided, the mathematical content appears to involve some kind of piecewise function. Let me summarize the different parts that I can interpret from the writing:

1. There are terms like \( x^2 + 5x + 6 \) and \( \frac{2 - 1}{5 - x} \).
2. It seems to be a piecewise function with different expressions based on conditions:
   - If \( x = -5 \)
   - If \( x > -5 \)
   - If \( x \leq -5 \)

The structure looks like a problem in which the function is defined differently based on the value of \( x \). I will try to clean up and interpret this further:

- For \( x \leq -5 \), there is an expression that might be \( \frac{2 - 1}{5 - x} \).
- For \( x > -5 \), it seems to involve \( x^2 + 5x + 6 \), which is a quadratic expression.

Could you clarify if there are specific questions or calculations you'd like help with related to this piecewise function? I can help break it down and solve any parts you need!

Would you like a more detailed explanation of how to handle such piecewise functions? Let me know if you'd like to dive deeper into specific sections or expressions.

Here are 5 related questions to consider:
1. How do you evaluate a piecewise function at a given value of \( x \)?
2. What does the condition \( x > -5 \) imply in terms of the quadratic expression?
3. Can you solve \( x^2 + 5x + 6 \) by factoring or using the quadratic formula?
4. What happens when \( x = -5 \) in the function \( \frac{2 - 1}{5 - x} \)?
5. How can you graph the different cases of this piecewise function?

**Tip**: When working with piecewise functions, always ensure that each part of the function is valid for the specified condition on \( x \). For instance, watch out for undefined expressions, like division by zero.

Given a piecewise function with different expressions based on conditions of x.

Explore a piecewise function involving quadratic and rational expressions based on different conditions of x. Learn to handle cases where x = -5, x > -5, and x ≤ -5, with a breakdown of key mathematical concepts and formulas. Ideal for students in Grades 9-11.

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