Goodwill and Other Intangible Assets (Changes in Goodwill Allocated to Segments) (Details) - USD ($) $ in Thousands	12 Months Ended
Aug. 31, 2020	Aug. 31, 2019
Goodwill [Roll Forward]
Beginning balance	$ 622,255	$ 627,745
Change in foreign currency exchange rates	13,241	(5,490)
Acquisitions and adjustments	61,357
Ending balance	696,853	622,255
EMS
Goodwill [Roll Forward]
Beginning balance	81,968	82,670
Change in foreign currency exchange rates	(138)	(702)
Acquisitions and adjustments	5,358
Ending balance	87,188	81,968
DMS
Goodwill [Roll Forward]
Beginning balance	540,287	545,075
Change in foreign currency exchange rates	13,379	(4,788)
Acquisitions and adjustments	55,999
Ending balance	$ 609,665	$ 540,287

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.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(1))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=120320667&loc=SL49117168-202975

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
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-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

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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.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
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-SubTopic 20
-Section 50
-Paragraph 1
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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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