Basic earnings per share are based on the weighted average number of common shares outstanding during the period. Diluted earnings per share are based on the weighted average number of common shares outstanding during the period adjusted to give effect to common stock equivalents.

The following table sets forth the computation of basic and diluted earnings per share for the periods indicated (in thousands, except per share data):

	Three months ended September 30,						Nine months ended September 30,
	2021			2020			2021			2020
Basic and Diluted:
Net income attributable to UHS	$	218,351		$	241,279		$	752,466		$	635,245
Less: Net income attributable to unvested restricted share grants		(396	)		(790	)		(1,609	)		(1,987	)
Net income attributable to UHS – basic and diluted	$	217,955		$	240,489		$	750,857		$	633,258

Weighted average number of common shares - basic		82,262			84,672			83,756			85,172
Net effect of dilutive stock options and grants based on the treasury stock method		1,411			575			1,275			415
Weighted average number of common shares and equivalents - diluted		83,673			85,247			85,031			85,587
Earnings per basic share attributable to UHS:	$	2.65		$	2.84		$	8.96		$	7.44
Earnings per diluted share attributable to UHS:	$	2.60		$	2.82		$	8.83		$	7.40

The “Net effect of dilutive stock options and grants based on the treasury stock method”, for all periods presented above, excludes certain outstanding stock options applicable to each period since the effect would have been anti-dilutive. The excluded weighted-average stock options totaled 4.1 million for the three months ended September 30, 2021 and 4.3 million for the nine months ended September 30, 2021. The excluded weighted-average stock options totaled 7.1 million for the three months ended September 30, 2020 and 6.7 million for the nine months ended September 30, 2020. All classes of our common stock have the same dividend rights.

During the three-month periods ended September 30, 2021 and 2020, pre-tax compensation cost of $14.6 million and $13.0 million, respectively, was recognized related to outstanding stock options. During the nine-month periods ended September 30, 2021 and 2020, pre-tax compensation costs of $44.8 million and $41.6 million, respectively, was recognized related to outstanding stock options. In addition, during the three-month periods ended September 30, 2021 and 2020, pre-tax compensation cost of approximately $3.5 million and $2.5 million, respectively, was recognized related to restricted stock awards and units. During the nine-month periods ended September 30, 2021 and 2020, pre-tax compensation costs of approximately $9.6 million and $7.3 million, respectively, was recognized related to restricted stock awards and units. As of September 30, 2021 there was approximately $144.6 million of unrecognized compensation cost related to unvested options and restricted stock awards and units which is expected to be recognized over the remaining weighted average vesting period of 2.8 years. There were 2,396,402 stock options granted during the first nine months of 2021 (including 406,952 stock options granted at a 10% market price premium) with a weighted-average grant date fair value of $39.66 per option. There were 150,860 shares of restricted shares and restricted units granted during the first nine months of 2021 with a weighted-average grant date fair value of $138.80 per share.

The expense associated with stock-based compensation arrangements is a non-cash charge. In the Condensed Consolidated Statements of Cash Flows, stock-based compensation expense is an adjustment to reconcile net income to cash provided by operating activities and aggregated to $55.5 million and $49.9 million during the nine-month periods ended September 30, 2021 and 2020.