To simplify the given expression, we will start by breaking it down into smaller parts:

Simplifying (√m-2)/(√m+2):
We multiply both the numerator and denominator by the conjugate of the denominator to rationalize the expression:
(√m-2)/(√m+2) * (√m-2)/(√m-2)
= (m-2√m-2√m+4)/(m-4)
= (m-4)/(m-4)
= 1

Simplifying (8√m)/(m-4):
This expression cannot be simplified further.

Simplifying (√m+2)/(m-2√m):
We multiply both the numerator and denominator by the conjugate of the denominator to rationalize the expression:
(√m+2)/(m-2√m) * (√m+2)/(√m+2)
= (m+2√m+2√m+4)/(m+2)
= (m+4)/(m+2)

Now we substitute these simplified expressions back into the original expression:
((√m-2)/(√m+2) + (8√m)/(m-4)) / ((√m+2)/(m-2√m))
= (1 + (8√m)/(m-4)) / ((m+4)/(m+2))
= (1 + (8√m)/(m-4)) * ((m+2)/(m+4))
= ((m+2) + 8√m) / (m-4)
= (m + 2 + 8√m) / (m - 4)

Therefore, the simplified expression is (m + 2 + 8√m) / (m - 4).