To simplify the expression, we need to find a common denominator for each set of fractions.

(11/22 - 5/9 - 1/6)
Common denominator for 22, 9, and 6 is 198.
(11/22 = 9/18), so the expression becomes:
(9/18 - 110/198 - 33/198)
= ((9 - 110 - 33)/198)
= (-134/198)

((4/5 - 3/4) - (5/6 - 3/4))
Common denominator for 5, 4, and 6 is 60.
((4/5) = (48/60)) and ((3/4) = (45/60)), so the expression becomes:
((48/60 - 45/60) - (50/60 - 45/60))
((3/60) - (5/60))
= (-2/60)
= (-1/30)

((17/8 - 3/4) - (5/6 - 3/4))
Common denominator for 8, 4, and 6 is 24.
((17/8) = (51/24)) and ((3/4) = (18/24)), so the expression becomes:
((51/24 - 18/24) - (20/24 - 18/24))
= ((33/24) - (2/24))
= (31/24)

Combining the results above:
((-134/198) - (-1/30) - (31/24))
= (-67/99 + 99/990 - 830/792)
= (-67/99 + 11/110 - 415/396)
= ((-2640 - 891 + 24750)/2772)
= (2145/2772)