Segment and Geographic Information - Segment Results Along with Reconciliation of Segment Profit to Income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020
Segment Reporting Information [Line Items]
Total segment revenues	$ 321,435	$ 345,753
Total segment profit	63,875	121,251
Corporate expenses and other, net	(26,388)	(31,115)
Stock-based compensation	(38,399)	(34,906)
Amortization of intangible assets	(11,969)	(14,793)
Acquisition-related costs, net	(1,248)	(325)
Restructuring and other charges, net	(8,506)	(8,566)
Other expenses, net	(11,374)	(22,289)
(Loss) income before income taxes	(34,009)	9,257
Healthcare
Segment Reporting Information [Line Items]
Revenues	200,400	199,332
Total segment revenues	200,400	199,332
Total segment profit	43,139	74,812
Enterprise
Segment Reporting Information [Line Items]
Revenues	117,227	139,152
Total segment revenues	117,227	139,152
Total segment profit	18,725	41,468
Other
Segment Reporting Information [Line Items]
Revenues	3,808	7,269
Total segment revenues	3,808	7,269
Total segment profit	$ 2,011	$ 4,971