https://r2.erweima.ai/mathbot/image/1725532134975w2psfrww.jpg

The image contains a mathematical expression. Let me transcribe it and provide a solution.

The expression appears to be:

\[
C = \frac{1}{\sqrt{x + 3}} - \frac{1}{\sqrt{x - 5}} + \frac{6}{x - 9}
\]
with conditions \(x \geq 0\), \(x \neq 9\), and \(x \neq 5\).

Let's break this down:
1. We are tasked with simplifying or analyzing this expression.
2. The domain restrictions are provided to avoid undefined values where the square roots are non-real and where division by zero might occur.

Would you like to simplify the expression or solve it for particular values of \(x\), or analyze the behavior further? Let me know!

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Here are some related questions to consider:
1. Would you like to analyze the domain of this function in more detail?
2. Should we explore the behavior of this expression as \(x\) approaches the restricted values (like \(x = 9\))?
3. Would you like to evaluate the expression for specific values of \(x\)?
4. Do you need help graphing the expression to understand its behavior visually?
5. Should we simplify each term further and check for possible cancellations?

**Tip:** When dealing with square roots, always ensure the values under the root are non-negative to avoid complex numbers!

Simplify or analyze the expression: C = (1 / √(x + 3)) - (1 / √(x - 5)) + (6 / (x - 9)), with the conditions x ≥ 0, x ≠ 9.

Explore how to simplify the expression C = (1 / √(x + 3)) - (1 / √(x - 5)) + (6 / (x - 9)), including handling domain restrictions, rational expressions, and square roots. Suitable for Grades 10-12.

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