P = {(x + 2√x - 7)/(x - 9) + (√x - 1)/(3 - √x)} : {1/(√x + 3) - 1/(√x - 1)}

It seems you have a mathematical expression that includes algebraic fractions involving square roots. Let's rewrite the expression more clearly first, breaking it down into manageable parts. You seem to have attempted to express a function or equation involving P, but it requires clarification.

1. Let's denote P:
\[
P = \frac{x + 2\sqrt{x} - 7}{x - 9} + \frac{\sqrt{x} - 1}{3 - \sqrt{x}}
\]

2. We also have another part referencing P:
\[
\frac{1}{\sqrt{x} + 3} - \frac{1}{\sqrt{x} - 1}
\]

The confusion may stem from trying to create an equality or a relationship between P and these other expressions. I’ll start by simplifying the expression for P.

**Step 1: Simplifying P**

The first term in P can be simplified directly. The second term requires a common denominator:

\[
\frac{x + 2\sqrt{x} - 7}{x - 9} + \frac{\sqrt{x} - 1}{3 - \sqrt{x}}
\]

To work with the second term, the common denominator will be:
\[
(3 - \sqrt{x})(x - 9)
\]

We can express everything over this common denominator, but it might be lengthy and complicated given the variables involved.

Instead, we can focus on each component separately for clarity.

**Step 2: Analyzing both parts**

Let's separately analyze the term before the equality sign:
- The first term is relatively straightforward, while the second term can be simplified using conjugates.

**Step 3: Finding a common ground**

You can factor or rationalize any square roots, then combine the terms. You will need to focus on ensuring the denominators are manageable.

If you want to equate these expressions, make sure they address the same variable conditions or clarify what you're aiming to solve or simplify.

If you need to equate or further break down the original conditions more specifically, please provide clear instructions on what you wish to achieve!