Let's simplify the expression step by step:

First, let's expand the squared term:

(x-2)² = (x-2)(x-2) = x² - 4x + 4

Now, substitute the value back into the expression:

x+2 - (x² - 4x + 4)/2
= x + 2 - (x²/2 - 2x + 2)
= x + 2 - x²/2 + 2x - 2

Let's find a common denominator for both terms:

1/x²-4 = 1/(x+2)(x-2)
1/x²-4x+4 = 1/(x-2)²

The common denominator will be (x+2)(x-2)²:

1/(x+2)(x-2) + 1/(x-2)²
= (x-2)/[(x+2)(x-2)] + (x+2)/(x-2)²
= (x-2 + (x+2)(x+2))/[(x+2)(x-2)²]
= (x-2 + x² + 4x + 2x + 4)/[(x+2)(x-2)²]
= (x² + 6x + 2)/[(x+2)(x-2)²]

Now we can substitute both simplified expressions back into the main expression:

(x + 2 - x²/2 + 2x - 2) * (x² + 6x + 2)/[(x+2)(x-2)²]

At this point, the expression is simplified as much as possible.