VHD disk compact

Hi,

I have installed Hyper V 2008R2 server. I have created a two VM. The Type of disk of both vm is .VHD.

My question is: VHD is unable to compact white spaces automatically from the disk and it could not reduce the vhd size after deletion the data. Is there any solution for it .

Can .VHDX type disk can help me  to reduce the white space automatically?

IS there any way or method to compact the vhd without down the VM

Please suggest me the solution to over come this monthly disk compact activity on my vms to reclaim the host disk space

Thanks