To simplify the given expression, let's break it down step by step:

1. Simplify the numerator:
- Start with the first term: (3√x + 3) / (x - 9)
- There is no way to simplify this further.
- Move on to the second term: 2√x / (√x + 3)
- Multiply both the numerator and denominator by (√x - 3) to rationalize the denominator:
(2√x * (√x - 3)) / ((√x + 3) * (√x - 3))
= (2√x * (√x - 3)) / (x - 9)
- Finally, simplify the third term: √x / (3 - √x)
- Multiply both the numerator and denominator by (3 + √x) to rationalize the denominator:
(√x * (3 + √x)) / ((3 - √x) * (3 + √x))
= (√x * (3 + √x)) / (9 - x)

So, the numerator becomes:
(3√x + 3) / (x - 9) - (2√x * (√x - 3)) / (x - 9) + (√x * (3 + √x)) / (9 - x)

2. Simplify the denominator:
(√x + 1) * (√x + 3)

3. Combine the numerator and denominator:
((3√x + 3) / (x - 9) - (2√x * (√x - 3)) / (x - 9) + (√x * (3 + √x)) / (9 - x)) / ((√x + 1) * (√x + 3))

Now, this is the simplified form of the given expression.