To simplify the expression

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

let's follow these steps:

### Step 1: Rewrite the Expression

The expression can be rewritten as:

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

### Step 2: Find a Common Denominator

The common denominator for the three terms is \((x - 2)(x + 2)\).

### Step 3: Combine the Fractions

Now we can combine the fractions:

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

### Step 4: Expand the Numerator

1. Expand \(x(x + 2)\):

\[
x(x + 2) = x^2 + 2x
\]

2. Expand \(2(x - 2)\):

\[
2(x - 2) = 2x - 4
\]

Substituting these expansions back into the numerator:

\[
x^2 - (x^2 + 2x) - (2x - 4)
\]

### Step 5: Simplify the Numerator

Combine the terms in the numerator:

\[
x^2 - x^2 - 2x - 2x + 4 = -4x + 4
\]

### Step 6: Write the Final Expression

So we have:

\[
\frac{-4x + 4}{(x - 2)(x + 2)}
\]

This can be factored further:

\[
\frac{-4(x - 1)}{(x - 2)(x + 2)}
\]

### Conclusion

The simplified form of the expression is:

\[
\frac{-4(x - 1)}{(x - 2)(x + 2)}
\]

To simplify the expression \( \frac{x^2}{(x - 2)(x + 2) - \frac{x}{x - 2} - \frac{2}{x + 2}} \), let's break it down step by step.

1. **Identify the expression:**
The expression can be rewritten (with proper parentheses) as:
\[
\frac{x^2}{(x - 2)(x + 2) - \frac{x}{x - 2} - \frac{2}{x + 2}}
\]

2. **Simplify the denominator:**
First, evaluate \( (x - 2)(x + 2) \):
\[
(x - 2)(x + 2) = x^2 - 4
\]

Therefore, the denominator becomes:
\[
x^2 - 4 - \frac{x}{x - 2} - \frac{2}{x + 2}
\]

3. **Combine the fractions in the denominator:**
We need a common denominator for the terms \( \frac{x}{x - 2} \) and \( \frac{2}{x + 2} \). The common denominator is \( (x - 2)(x + 2) \):
\[
\frac{x}{x - 2} = \frac{x(x + 2)}{(x - 2)(x + 2)} = \frac{x^2 + 2x}{x^2 - 4}
\]
\[
\frac{2}{x + 2} = \frac{2(x - 2)}{(x - 2)(x + 2)} = \frac{2x - 4}{x^2 - 4}
\]
Therefore, we can now write the two fractions together:
\[
-\frac{x^2 + 2x + 2x - 4}{x^2 - 4} = -\frac{x^2 + 4x - 4}{x^2 - 4}
\]

4. **Putting it back into the denominator:**
Now we have:
\[
x^2 - 4 - \left(-\frac{x^2 + 4x - 4}{x^2 - 4}\right) = \frac{(x^2 - 4)(x^2 - 4) + x^2 + 4x - 4}{x^2 - 4}
\]
Simplifying the numerator will yield:
\[
(x^2 - 4)^2 + x^2 + 4x - 4
\]

5. **Resulting expression:**
The entire expression, now simplified, is:
\[
\frac{x^2}{\frac{(x^2 - 4)^2 + x^2 + 4x - 4}{x^2 - 4}} = \frac{x^2 (x^2 - 4)}{(x^2 - 4)^2 + x^2 + 4x - 4}
\]

Now, further simplification depends on the specific values of \( x \). The above process illustrates the required steps to reduce and combine such expressions.

Simplifying completely might require factoring or possibly identifying specific values for \( x \). If there's more specification on the values or further simplification is needed, please provide.