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Goodwill and Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of intangible assets	$ 10.2	$ 10.2	$ 30.8	$ 30.4
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Amortization expense in fiscal 2022	41.2		41.2
Amortization expense in fiscal 2023	40.5		40.5
Amortization expense in fiscal 2024	40.0		40.0
Amortization expense in fiscal 2025	31.9		31.9
Amortization expense in fiscal 2026	$ 29.1		$ 29.1

X

- Definition

Finite-Lived Intangible Asset, Expected Amortization, Current Fiscal Year

+ References

No definition available.

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- Definition

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

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-Topic 350
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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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