To simplify the expression, we need to find a common denominator for the fractions. The common denominator for x^2 - 4 and x(x + 2) is x(x + 2)(x - 2).

Now, let's rewrite the expression with the common denominator:

(x(x + 2)(x - 2))/(x^2 - 4) - 2(x - 2)/(x(x + 2))

Next, let's simplify each fraction separately.

For the first fraction, x(x + 2)(x - 2)/(x^2 - 4), we can factor the denominator as the difference of squares:

(x(x + 2)(x - 2))/((x + 2)(x - 2))

The (x - 2) terms cancel out, leaving us with:

x(x)/(x + 2)

Simplifying further, we have:

x^2/(x + 2)

For the second fraction, 2(x - 2)/(x(x + 2)), we can simplify by canceling out common factors:

2(x - 2)/(x(x + 2)) = 2/(x + 2)

Now, let's rewrite the simplified fractions:

x^2/(x + 2) - 2/(x + 2)

Since the denominators are the same, we can combine the numerators:

(x^2 - 2)/(x + 2)

Therefore, the simplified expression is (x^2 - 2)/(x + 2).