To simplify the expression

\[
\left( \frac{1}{\sqrt{x-3}} + \frac{1}{\sqrt{x+3}} \right) \cdot \left( 1 - \frac{3}{\sqrt{x}} \right),
\]

let’s break it down into parts.

### Step 1: Combine the first part
The first part is:

\[
\frac{1}{\sqrt{x-3}} + \frac{1}{\sqrt{x+3}}.
\]

To combine these fractions, we need a common denominator, which is \(\sqrt{x-3} \cdot \sqrt{x+3}\):

\[
\frac{\sqrt{x+3} + \sqrt{x-3}}{\sqrt{x-3}\sqrt{x+3}}.
\]

### Step 2: Rewrite the second part
The second part is:

\[
1 - \frac{3}{\sqrt{x}} = \frac{\sqrt{x} - 3}{\sqrt{x}}.
\]

### Step 3: Multiply the two parts together
Now we multiply:

\[
\frac{\sqrt{x+3} + \sqrt{x-3}}{\sqrt{x-3}\sqrt{x+3}} \cdot \frac{\sqrt{x}-3}{\sqrt{x}}.
\]

This gives:

\[
\frac{(\sqrt{x+3} + \sqrt{x-3})(\sqrt{x} - 3)}{\sqrt{x-3}\sqrt{x+3}\sqrt{x}}.
\]

### Final Expression
Thus, the simplified expression is:

\[
\frac{(\sqrt{x+3} + \sqrt{x-3})(\sqrt{x} - 3)}{\sqrt{x-3}\sqrt{x+3}\sqrt{x}}.
\]

### Conclusion
This is the final simplified form of your expression. If you need further simplification or calculation, we can explore that too!