Unable to claim 100G Free Space Partition after Deleting Yosemite Beta

Question

When I was running Mavericks I had a single large 500G volume (no partitions). The I installed Yosemite Beta on a 100G partition. After Yosemite was released it reinstalled over the Mavericks on Partition 1. When I tried to delete Yosemite Beta partition to reclaim the space to evert to original form - I have been stuck with a 100G Free Space partition that I can do nothing with  - neither make it into a usable volume to store data nor be able to merge it into the original partition. I am hitting up against the space restrictions dn desperate now - I have see Loner T do an awesome job with his advice on this forum for similar issues. Very grateful for help. I also purchase iPartition but it was a waste as it says that it does not have write access to the disk.

sunkap · Answer

Here are my Diskutil listDads-Mac:~ sunkap$ diskutil list/dev/disk0   #:                       TYPE NAME                    SIZE       IDENTIFIER   0:      GUID_partition_scheme                        *500.3 GB   disk0   1:                        EFI EFI                     209.7 MB   disk0s1   2:                  Apple_HFS                         399.4 GB   disk0s2   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3/dev/disk1   #:                       TYPE NAME                    SIZE       IDENTIFIER   0:                  Apple_HFS Mac                    *399.4 GB   disk1                                 Logical Volume on disk0s2                                 D30FABC9-09A2-47B8-B008-7AE0CBB42164                                 UnencryptedDads-Mac:~ sunkap$

Loner T · Answer

Can you also post the output of diskutil cs listsudo gpt -vv -r show /dev/disk0