To simplify the expression

\[
\frac{x^3 + 2x^2\sqrt{x} - 2x\sqrt{x} - x}{(x - \sqrt{x})(x + \sqrt{x})\sqrt{x}},
\]

let's start simplifying the numerator:

1. **Rearranging the numerator**:
\[
x^3 - x + 2x^2\sqrt{x} - 2x\sqrt{x} = x^3 - x + 2\sqrt{x}(x^2 - x).
\]

2. **Factoring out common terms**:
\[
x^2 - x = x(x - 1).
\]
So, we rewrite the numerator:
\[
x^3 - x + 2\sqrt{x}(x(x - 1)).
\]

Thus, the numerator becomes:
\[
x^3 - x + 2x\sqrt{x}(x - 1).
\]

3. **Now combine the terms**:
Begin by attempting simple factorization for \(x^3 - x\) first:
\[
x^3 - x = x(x^2 - 1) = x(x - 1)(x + 1).
\]

Now the numerator can be expressed as:
\[
x(x - 1)(x + 1) + 2\sqrt{x}x(x - 1).
\]

Factor out \(x(x - 1)\):
\[
x(x - 1)\left((x + 1) + 2\sqrt{x}\right).
\]

4. **Substitute back into the original expression**:
The complete expression now is:
\[
\frac{x(x - 1)((x + 1) + 2\sqrt{x})}{(x - \sqrt{x})(x + \sqrt{x})\sqrt{x}}.
\]

5. **Now focus on the denominator**:
\[
(x - \sqrt{x})(x + \sqrt{x}) = x^2 - (\sqrt{x})^2 = x^2 - x = x(x - 1).
\]
Therefore, the denominator can be rewritten as:
\[
x(x - 1)\sqrt{x}.
\]

6. **Final simplification**:
Now write the whole expression:
\[
\frac{x(x - 1)((x + 1) + 2\sqrt{x})}{x(x - 1)\sqrt{x}}.
\]

Assuming \(x(x - 1) \neq 0\) (i.e., \(x \neq 0\) and \(x \neq 1\)), we can cancel \(x(x - 1)\) from both the numerator and the denominator:
\[
\frac{(x + 1) + 2\sqrt{x}}{\sqrt{x}}.
\]

Finally, we can further simplify this to:
\[
\frac{x + 1}{\sqrt{x}} + 2 = \frac{x + 1 + 2\sqrt{x}}{\sqrt{x}}.
\]

Thus, the simplified final expression is:
\[
\frac{x + 1 + 2\sqrt{x}}{\sqrt{x}}.
\]