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Acquired Intangible Assets and Goodwill
 9 Months Ended
Sep. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract]  
Acquired Intangible Assets and Goodwill Acquired Intangible Assets and Goodwill
Acquired Intangible Assets—The gross carrying amounts and accumulated amortization of intangible assets were as follows:

September 30, 2022December 31, 2021
Weighted-Average Useful Lives (Years)GrossAccumulated AmortizationNetGrossAccumulated AmortizationNet
Trade names
9.3
$82,690 $(12,497)$70,193 $71,040 $(6,004)$65,036 
Developed technology
3.3
66,340 (33,111)33,229 63,480 (17,285)46,195 
Customer relationships1081,360 (12,763)68,597 81,360 (6,662)74,698 
Total$230,390 $(58,371)$172,019 $215,880 $(29,951)$185,929 

Amortization expense amounted to $9,747 and $8,926 for the three months ended September 30, 2022 and 2021, respectively, and $28,420 and $17,974 for the nine months ended September 30, 2022 and 2021, respectively.

Our estimate of remaining amortization expense for intangible assets that existed as of September 30, 2022 is as follows:

2022, excluding the nine months ended September 30, 2022
$9,747 
202338,988 
202423,741 
202517,618 
202617,380 
Thereafter64,545 
Estimated remaining amortization expense$172,019 
Goodwill—The carrying amounts of goodwill by reportable segment were as follows:

Real Estate ServicesRentalsMortgageTotal
Balance as of December 31, 2021
$250,231 $159,151 $— $409,382 
Goodwill resulting from acquisition— — 51,967 51,967 
Balance as of September 30, 2022
$250,231 $159,151 $51,967 $461,349