One of Date Island Solutions.sql

CREATE TABLE [dbo].[RentalInvoice](
 [InvoiceId] [int] IDENTITY(1,1) NOT NULL,
 [InvoiceNo] [varchar](15) NOT NULL,
 [InvoiceDate] [date] NOT NULL,
 [RentalId] [int] NOT NULL,
 [StartDate] [date] NOT NULL,
 [EndDate] [date] NOT NULL,
 CONSTRAINT [PK_RentalInvoice] PRIMARY KEY CLUSTERED
 (
 [InvoiceId] ASC
 )WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
 ) ON [PRIMARY]
 GO
    
 SET IDENTITY_INSERT [dbo].[RentalInvoice] ON
 GO
 INSERT [dbo].[RentalInvoice] ([InvoiceId], [InvoiceNo], [InvoiceDate], [RentalId], [StartDate], [EndDate]) VALUES (1, N'A1', CAST(N'2022-01-15' AS Date), 1, CAST(N'2022-01-10' AS Date), CAST(N'2022-01-31' AS Date))
 GO
 INSERT [dbo].[RentalInvoice] ([InvoiceId], [InvoiceNo], [InvoiceDate], [RentalId], [StartDate], [EndDate]) VALUES (2, N'A2', CAST(N'2022-02-06' AS Date), 2, CAST(N'2022-02-02' AS Date), CAST(N'2022-02-06' AS Date))
 GO
 INSERT [dbo].[RentalInvoice] ([InvoiceId], [InvoiceNo], [InvoiceDate], [RentalId], [StartDate], [EndDate]) VALUES (3, N'A3', CAST(N'2022-03-11' AS Date), 3, CAST(N'2022-03-01' AS Date), CAST(N'2022-03-10' AS Date))
 GO
 INSERT [dbo].[RentalInvoice] ([InvoiceId], [InvoiceNo], [InvoiceDate], [RentalId], [StartDate], [EndDate]) VALUES (4, N'A4', CAST(N'2022-04-15' AS Date), 4, CAST(N'2022-04-01' AS Date), CAST(N'2022-04-15' AS Date))
 GO
 INSERT [dbo].[RentalInvoice] ([InvoiceId], [InvoiceNo], [InvoiceDate], [RentalId], [StartDate], [EndDate]) VALUES (6, N'A4', CAST(N'2022-04-25' AS Date), 4, CAST(N'2022-04-20' AS Date), CAST(N'2022-04-25' AS Date))
 GO
 SET IDENTITY_INSERT [dbo].[RentalInvoice] OFF
 GO
    
 CREATE TABLE [dbo].[Rental](
 [RentalId] [int] IDENTITY(1,1) NOT NULL,
 [RentalContract] [varchar](50) NOT NULL,
 [StartDate] [date] NOT NULL,
 [EndDate] [date] NOT NULL,
 CONSTRAINT [PK_Rental] PRIMARY KEY CLUSTERED
 (
 [RentalId] ASC
 )WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
 ) ON [PRIMARY]
 GO
    
 SET IDENTITY_INSERT [dbo].[Rental] ON
 GO
 INSERT [dbo].[Rental] ([RentalId], [RentalContract], [StartDate], [EndDate]) VALUES (1, N'C1', CAST(N'2022-01-01' AS Date), CAST(N'2022-01-31' AS Date))
 GO
 INSERT [dbo].[Rental] ([RentalId], [RentalContract], [StartDate], [EndDate]) VALUES (2, N'C2', CAST(N'2022-02-01' AS Date), CAST(N'2022-02-15' AS Date))
 GO
 INSERT [dbo].[Rental] ([RentalId], [RentalContract], [StartDate], [EndDate]) VALUES (3, N'C3', CAST(N'2022-03-01' AS Date), CAST(N'2022-03-31' AS Date))
 GO
 INSERT [dbo].[Rental] ([RentalId], [RentalContract], [StartDate], [EndDate]) VALUES (4, N'C4', CAST(N'2022-04-01' AS Date), CAST(N'2022-04-30' AS Date))
 GO
 SET IDENTITY_INSERT [dbo].[Rental] OFF
 GO
    
 ;WITH Num1 (n) AS (
 SELECT 1 as n
 UNION ALL SELECT n+1 as n
 FROM Num1 Where n <101),
 Num2 (n) AS (SELECT 1 FROM Num1 AS X, Num1 AS Y), 
 Nums (n) AS (SELECT ROW_NUMBER() OVER(ORDER BY n) FROM Num2)
     
 ,mycteRental as ( 
  Select  RentalId,[RentalContract], dateadd(day,n-1,StartDate) dt  
  from [Rental]
  Cross apply (select n from nums ) d(n)
  where  dateadd(day,n-1,StartDate)  <= [EndDate]
 )
    
 ,mycteRentalInvoice as (
   Select  RentalId, dateadd(day,n-1,StartDate) dt  
   from [RentalInvoice]
  Cross apply (select n from nums ) d(n)
  where  dateadd(day,n-1,StartDate)  <= [EndDate]
 )
 ,mycteFindIsland as (
 select *,DATEADD(DAY, - ROW_NUMBER() OVER(PARTITION BY RentalId ORDER BY dt), dt) AS grp 
 from mycteRental m1
 where not exists 
 (select 1 from mycteRentalInvoice m2 where m1.RentalId=m2.RentalId and m1.dt=m2.dt) 
 )
 ,mycteFindFirstIsland as (
 select *,dense_rank() OVER(PARTITION BY RentalId  Order by grp) dnk 
 from mycteFindIsland
 )
 select RentalId,RentalContract, min(dt) StartDate, max(dt) EndDate
 from mycteFindFirstIsland
 where dnk=1 -- get first
 group by RentalId,RentalContract
     
     
 drop table [dbo].[RentalInvoice],   [dbo].[Rental]