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Reportable Segments and Geographic Information - Schedule of Reconciles Total Segment Attributable Earnings Before Taxes and Amortization to Income From Continuing Operations Before Taxes (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2023
Segment Reporting [Abstract] |  |  |
Total segment attributable earnings before taxes and amortization | $ 1,181,300 | $ 1,046,400 | $ 642,400
Corporate general and administrative expenses | (148,900) | (145,100) | (141,000)
Restructuring and acquisition costs | (59,355) | (98,918) | (188,404)
Other income | (2,500) | 2,100 | (5,300)
Interest income | 62,894 | 58,560 | 40,251
Interest expense | (184,304) | (185,420) | (159,342)
Amortization expense | (2,200) | (18,800) | (18,600)
Income attributable to noncontrolling interests from continuing operations | 68,700 | 59,300 | 43,300
Income from continuing operations before taxes | $ 915,569 | $ 718,152 | $ 213,400

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