Rút gọn √9 - 3√8 - \(\frac{-√3 - 1}{√2}\) + √5 - 2√6 - √2 - √3

To simplify the expression

\[
\sqrt{9} - 3\sqrt{8} - \frac{-\sqrt{3} - 1}{\sqrt{2}} + \sqrt{5} - 2\sqrt{6} - \sqrt{2} - \sqrt{3},
\]

let's start calculating each component step by step:

1. **Calculate the square roots:**
- \(\sqrt{9} = 3\)
- \(\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\), thus \(3\sqrt{8} = 3 \cdot 2\sqrt{2} = 6\sqrt{2}\)

2. **Simplifying the fraction:**
- \(\frac{-\sqrt{3} - 1}{\sqrt{2}} = -\frac{\sqrt{3}}{\sqrt{2}} - \frac{1}{\sqrt{2}} = -\sqrt{\frac{3}{2}} - \frac{1}{\sqrt{2}}\)

3. **For \(\sqrt{5}\) and \(2\sqrt{6}\):**
- These will stay as they are for the moment.
- \(\sqrt{6}\) cannot be simplified easily, so it remains \(2\sqrt{6}\).

4. **Combine all parts:**
The expression now looks like this:
\[
3 - 6\sqrt{2} + \sqrt{5} - 2\sqrt{6} - \sqrt{2} - \sqrt{3} + \sqrt{\frac{3}{2}} + \frac{1}{\sqrt{2}}.
\]

5. **Re-organize and combine like terms:**
- Combine the like terms involving \(\sqrt{2}\):
- The coefficients for \(\sqrt{2}\) are: \(-6 - 1 + \frac{1}{\sqrt{2}}\).
- This gives us: \(-7\sqrt{2} + \frac{1}{\sqrt{2}}\).

6. **Collect all terms together:**
\[
3 + \sqrt{5} - 2\sqrt{6} - 7\sqrt{2} - \sqrt{3} + \sqrt{\frac{3}{2}}.
\]

This simplification doesn't yield a neat integer or simple radical; thus, the final expression remains somewhat complex and depends on specific numerical values for the radicals for further rationalization or simplification.

Therefore, the simplified version of the expression without numerical evaluation of the radicals is:
\[
3 + \sqrt{5} - 2\sqrt{6} - 7\sqrt{2} - \sqrt{3} + \sqrt{\frac{3}{2}}.
\]