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Income Taxes - Effective Rate Reconciliation (Details)
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Income Tax Disclosure [Abstract]      
Federal statutory rate effect of: 21.00% 21.00% 21.00%
U.S. State and local income taxes 1.80% 1.20% (0.90%)
Foreign earnings and losses taxed at different rates 1.00% 0.90% 0.20%
Change in valuation allowance 1.90% 1.00% 0.90%
Income tax rate holiday (0.50%) (0.80%) 0.50%
U.S. permanent items (1.20%) 0.60% (0.50%)
Non-deductible compensation 1.90% 0.60% 0.70%
Foreign permanent items (0.20%) 1.10% 0.20%
U.S. bargain purchase gain (0.50%) (8.30%) (1.00%)
GILTI 0.60% 0.70% 2.20%
Income tax rate change (1.20%) 0.00% 0.00%
Income tax rate change 24.60% 18.00% 23.30%