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Concentration of Risk and Segment Data - Segment Income (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Feb. 28, 2018
Feb. 28, 2017
Feb. 28, 2018
Feb. 28, 2017
Reconciling items:        
Amortization of intangibles $ (9,890) $ (8,766) $ (19,869) $ (17,088)
Stock-based compensation expense and related charges (15,039) (15,318) (67,784) (15,027)
Restructuring and related charges (5,427) (44,927) (16,815) (80,829)
Other expense (10,485) (3,371) (16,367) (8,051)
Interest income 5,011 2,289 8,824 4,744
Interest expense (37,796) (33,800) (74,042) (66,644)
Income before income tax 86,262 48,301 193,701 178,839
Operating Segments        
Reconciling items:        
Income before income tax 178,596 152,194 405,816 361,734
Segment Reconciling Items        
Reconciling items:        
Distressed customer charge (14,706) 0 (14,706) 0
Stock-based compensation expense and related charges (15,039) (15,318) (67,784) (15,027)
Business interruption and impairment charges, net (4,002) 0 (11,356) 0
EMS        
Reconciling items:        
Restructuring and related charges (2,100) (4,000) (8,000) (11,300)
EMS | Operating Segments        
Reconciling items:        
Income before income tax 95,283 98,089 180,993 187,635
DMS        
Reconciling items:        
Restructuring and related charges (3,300) (36,600) (7,900) (48,100)
DMS | Operating Segments        
Reconciling items:        
Income before income tax $ 83,313 $ 54,105 $ 224,823 $ 174,099