Let's carefully look at the expression you are asking about:

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

It seems like you want to simplify an expression that involves two terms in the denominator. However, the usage of "and" in this context is unclear. Could you clarify whether you meant the sum of two terms in the denominator, or if you intended something else?

If you meant the sum of two square root terms in the denominator (e.g., $\sqrt{2x-1} + \sqrt{2x-1}$), then the simplification would follow a similar process as explained earlier.

Please confirm your intended expression so I can help you with the correct simplification.