Concentration of Risk and Segment Data (Segment Income) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2019	Aug. 31, 2018	Aug. 31, 2017
Reconciling items:
Amortization of intangibles	$ (31,923)	$ (38,490)	$ (35,524)
Stock-based compensation expense and related charges	(61,346)	(98,511)	(48,544)
Restructuring and related charges	(25,914)	(36,902)	(160,395)
Distressed customer charges	(6,235)	(32,710)	(10,198)
Business interruption and impairment charges, net	2,860	(11,299)	0
Acquisition and integration charges	(52,697)	(8,082)	0
Loss on disposal of subsidiaries	0	0	(2,112)
Restructuring of securities loss	(29,632)	0	0
Other expense	(53,750)	(37,563)	(28,448)
Interest income	21,460	17,813	12,525
Interest expense	(188,730)	(149,002)	(138,074)
Income before income tax	450,704	373,401	256,233
Cayey, Puerto Rico
Reconciling items:
Insurance proceeds from Hurricane Maria	2,900	24,900
Operating Segments
Reconciling items:
Income before income tax	876,611	768,147	667,003
EMS
Reconciling items:
Restructuring and related charges	(21,500)	(16,300)	(51,300)
EMS | Operating Segments
Reconciling items:
Income before income tax	480,047	451,149	436,110
DMS
Reconciling items:
Restructuring and related charges	(2,600)	(16,600)	(82,400)
DMS | Operating Segments
Reconciling items:
Income before income tax	$ 396,564	$ 316,998	$ 230,893