Yes, the expression $\frac{x+1}{\sqrt{2x-1} + \sqrt{2x-1}}$ can be simplified. Let's go through the steps:

Given Expression:

$\frac{x+1}{\sqrt{2x-1} + \sqrt{2x-1}}$

Step 1: Combine Like Terms

The denominator consists of two identical square roots added together: $\sqrt{2x-1} + \sqrt{2x-1} = 2\sqrt{2x-1}$

Step 2: Simplify the Expression

Now, substitute this simplification into the original expression: $\frac{x+1}{2\sqrt{2x-1}}$

Thus, the simplified expression is: $\frac{x+1}{2\sqrt{2x-1}}$

This is the most simplified form of the given expression.

Would you like more details or have any questions?

Here are some related questions:

1. How would you rationalize the denominator of a fraction involving square roots?
2. What are the restrictions on $x$ for the expression $\sqrt{2x-1}$?
3. Can this simplified expression be further factored for specific values of $x$?
4. How does this simplification affect the behavior of the function as $x$ approaches infinity?
5. How would you apply this simplification in solving equations?

Tip: When simplifying expressions with square roots, always look for ways to combine like terms or rationalize the denominator for further simplification.