https://file.aiquickdraw.com/mathbot/file/17263199404980h2nxsca.jpg

The expression in the image is as follows:

\[
\sqrt{(1 - x)} \cdot \frac{1}{2} \cdot (1 + x)^{-\frac{1}{2}} + \frac{1}{2} \cdot (1 - x)^{-\frac{1}{2}} \cdot \sqrt{(1 + x)}
\]

This appears to involve square roots, powers, and products of terms involving \( (1 - x) \) and \( (1 + x) \).

Would you like me to simplify or differentiate this expression? Let me know how you'd like to proceed.

Here are five questions related to this expression:
1. What mathematical technique would you use to simplify a product of square roots and powers?
2. How can this expression be rewritten using exponent rules for negative powers?
3. What would happen if you differentiated this expression with respect to \( x \)?
4. Are there any special cases for the values of \( x \) where the expression simplifies significantly?
5. What is the domain of this expression based on the square roots and negative powers?

**Tip**: When simplifying expressions with square roots, remember that \( \sqrt{a} = a^{1/2} \), and it can be helpful to convert everything to powers for easier manipulation.

Simplify or differentiate the following mathematical expression: sqrt(1 - x) * (1 + x)^(-1/2) + (1 - x)^(-1/2) * sqrt(1 + x).

Learn how to simplify or differentiate expressions involving square roots and negative powers. The expression sqrt(1 - x) * (1 + x)^(-1/2) + (1 - x)^(-1/2) * sqrt(1 + x) is explored, covering key algebraic concepts and exponent rules. Suitable for students in Grades 11-12.

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