Property and Equipment, net- Schedule of property and equipment (Details) - USD ($) $ in Thousands	9 Months Ended
Jun. 30, 2022	Sep. 30, 2021
Property, Plant and Equipment [Line Items]
Right-of-use assets for finance leases	$ 215	$ 215
Property and equipment and Right-of-use assets for finance leases, gross	398,673	309,840
Less: Accumulated depreciation and amortization	(191,637)	(187,789)
Property and equipment and Right-of-use assets for finance leases, net	207,036	122,051
Land
Property, Plant and Equipment [Line Items]
Property and equipment, gross	16,603	8,355
Buildings and building improvements
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 118,702	71,036
Buildings and building improvements \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	3 years
Buildings and building improvements \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	35 years
Leasehold improvements
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 78,383	63,502
Leasehold improvements \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	1 year
Leasehold improvements \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	28 years
Training equipment
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 93,370	91,191
Training equipment \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	3 years
Training equipment \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	10 years
Office and computer equipment
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 31,273	31,718
Office and computer equipment \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	3 years
Office and computer equipment \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	10 years
Curriculum development
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	5 years
Property and equipment, gross	$ 20,130	19,692
Software developed for internal use
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 11,887	12,524
Software developed for internal use \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	1 year
Software developed for internal use \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	5 years
Vehicles
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	5 years
Property and equipment, gross	$ 1,428	1,436
Right-of-use assets for finance leases \| Minimum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	2 years
Right-of-use assets for finance leases \| Maximum
Property, Plant and Equipment [Line Items]
Depreciable Lives (in years)	3 years
Construction in progress
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 26,682	$ 10,171

Amount, before accumulated amortization, of right-of-use asset from finance lease.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

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+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
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Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
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+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
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Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
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+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
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