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Other (Income) Expense, Net (Schedule of Other (Income) Expense, Net) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Equity interest in the earnings of the JV | $ (41,191) | $ (36,846) | $ (18,193)
Net (gain) loss on sales of assets and businesses | (457) | 1,491 | (1,775)
Gain on non-recurring matter related to a previous acquisition | (4,803) |  |
Rent income | (347) | (360) | (672)
Net (gain) loss on investments in deferred compensation program | (6,571) | (3,265) | 6,295
Other components of net periodic pension and other postretirement benefit, excluding service cost and interest expense | 11,764 | 10,547 | 11,572
Other | (2,035) | (764) | (774)
Other (income) expense, net | $ (67,168) | $ (50,291) | $ (26,691)

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