https://file.aiquickdraw.com/mathbot/file/1727072224266vslh0wgl.jpg

The expression in the image appears to be:

\[
\frac{x - 5}{\sqrt{x} - \sqrt{5}}
\]

Would you like to simplify this expression, or is there another operation you'd like to perform on it? Let me know if you'd like a detailed explanation or solution!

Here are 5 related questions that might expand this concept:
1. How do you rationalize a denominator involving square roots?
2. What is the limit of this expression as \(x\) approaches 5?
3. Can you factor any part of this expression further?
4. How does this expression behave for large values of \(x\)?
5. How does this type of fraction relate to solving equations involving square roots?

**Tip**: When simplifying expressions with square roots, multiplying by the conjugate can help eliminate the square roots in the denominator.

Simplify the expression \(\frac{x - 5}{\sqrt{x} - \sqrt{5}}\).

Learn how to simplify the expression \(\frac{x - 5}{\sqrt{x} - \sqrt{5}}\) by rationalizing the denominator. This algebraic problem covers square root properties and the conjugate method, suitable for students in Grades 10-12.

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