The given expression is:

\[
\frac{\sqrt{2x+1}}{\sqrt{x-1}}
\]

This expression involves two square roots. There is no immediate simplification unless you want to manipulate it further, but here's a step-by-step breakdown:

### 1. Domain of the Expression:
For the square roots to be valid, the expressions inside them must be non-negative.

- \( \sqrt{2x+1} \) is defined when \( 2x + 1 \geq 0 \), meaning \( x \geq -\frac{1}{2} \).
- \( \sqrt{x-1} \) is defined when \( x-1 \geq 0 \), meaning \( x \geq 1 \).

Therefore, the domain of the expression is \( x \geq 1 \).

### 2. Simplification:
You can leave the expression as it is unless you'd like to perform more operations, like rationalizing the denominator or manipulating it for specific purposes.

Would you like to simplify it further or solve a specific equation involving this expression?

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If you'd like more details or explanations, feel free to ask! Here are some related questions to explore further:

1. What is the derivative of this expression?
2. How can you rationalize the denominator of this expression?
3. What happens when you substitute specific values of \( x \) into this expression?
4. How would you evaluate the limits of this expression as \( x \to 1 \)?
5. What is the range of the expression?

**Tip:** Always check the domain before simplifying expressions involving square roots!

Explore how to simplify the radical expression √(2x+1)/√(x-1) and find its domain. Understand key concepts like the square root theorem and domain restrictions. This step-by-step guide is perfect for students in Grades 10-12.

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