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Goodwill and Intangible Assets - Amortization (Details) - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
May 31, 2025 | May 31, 2024 | May 31, 2025 | May 31, 2024 | Aug. 31, 2024
Goodwill and Intangible Assets Disclosure [Abstract] |  |  |  |  |
Amortization related to intangible assets | $ 153,199 | $ 133,097 | $ 465,575 | $ 364,353 |
Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract] |  |  |  |  |
Remainder of 2025 | 150,397 |  | 150,397 |  |
2026 | 563,620 |  | 563,620 |  |
2027 | 496,707 |  | 496,707 |  |
2028 | 459,216 |  | 459,216 |  |
2029 | 366,312 |  | 366,312 |  |
Thereafter | 555,433 |  | 555,433 |  |
Net Carrying Amount | $ 2,591,685 |  | $ 2,591,685 |  | $ 2,904,031

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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 -Name Accounting Standards Codification -Section 45 -Paragraph 28 -Subparagraph (b) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-28 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Section 55 -Paragraph 40 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482640/350-30-55-40 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482665/350-30-50-2 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Section 45 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482686/350-30-45-2 + Details
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- Definition 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://www.xbrl.org/2003/role/exampleRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Section 55 -Paragraph 40 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482640/350-30-55-40 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 350 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482665/350-30-50-2 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 985 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147481283/985-20-50-2 + Details
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