To simplify the expression A, we can start by simplifying each individual term.

1. Simplifying the first term: √x/√(x+2)
To simplify this term, we can rationalize the denominator by multiplying both the numerator and denominator by √(x+2):
(√x/√(x+2)) * (√(x+2)/√(x+2)) = √(x(x+2))/(x+2) = √(x^2 + 2x)/(x+2)

2. Simplifying the second term: 2/√(x-2)

3. Simplifying the third term: (x-4)/√(x+2)

Now, we can substitute these simplified terms back into the original expression A:

A = (√(x^2 + 2x)/(x+2) + 2/√(x-2)) / ((x-4)/√(x+2))

To simplify further, we can multiply the numerator and denominator by the common denominator √(x+2):

A = (√(x^2 + 2x) + 2√(x+2)(x+2)) / ((x-4)√(x+2))

Simplifying the numerator:

A = (√(x^2 + 2x) + 2(x+2)) / ((x-4)√(x+2))

A = (√(x^2 + 2x) + 2x + 4) / ((x-4)√(x+2))

Therefore, the simplified expression for A is (√(x^2 + 2x) + 2x + 4) / ((x-4)√(x+2)).