Goodwill and Other Intangible Assets (Changes in Goodwill Allocated to Segments) (Details) - USD ($) $ in Thousands	12 Months Ended
Aug. 31, 2019	Aug. 31, 2018
Goodwill [Roll Forward]
Beginning balance	$ 627,745	$ 608,184
Acquisitions and adjustments		22,577
Change in foreign currency exchange rates	(5,490)	(3,016)
Ending balance	622,255	627,745
EMS
Goodwill [Roll Forward]
Beginning balance	82,670	52,574
Acquisitions and adjustments		30,763
Change in foreign currency exchange rates	(702)	(667)
Ending balance	81,968	82,670
Goodwill reallocated		8,200
DMS
Goodwill [Roll Forward]
Beginning balance	545,075	555,610
Acquisitions and adjustments		(8,186)
Change in foreign currency exchange rates	(4,788)	(2,349)
Ending balance	$ 540,287	545,075
Goodwill reallocated		$ (8,200)

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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-Publisher FASB
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Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination.

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Amount of foreign currency translation gain (loss) which increases (decreases) an asset representing future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Amount of transfers into (out of) an asset representing the future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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