how do I delete photos that don't have a trash can

Only photos that have been taken with the device camera or have been saved to Photos can be deleted directly on the device. Photos, that do not show a trash can button, are probably photos that have been synced to the device from a computer. These photos are not imported and saved in the Photos Library but stored differently.Usually these photos are shown in the album "from my Mac". To delete synced photos you have simply to sync again. This will replace the synced photos by the newly synced photos. Sync again, and set the checkmark to sync photos, but do not select any albums.

Are you using a Mac or a PC? On a Mac see this document: Sync your photos manually using the Finder - Apple Support (the paragraph "Stop syncing ... albums").

If you have been syncing a PC with iTunes, sync again with iTunes. Sync photos in iTunes on PC with devices - Apple Support

JBS69 Said:

"how do I delete photos that don't have a trash can: I have photos and videos in my iPhone library that do not have a trash can icon so that I can delete them"

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Successfully Deleting Photos:

Perform as instructed here, including creating backup: Delete Photos on your iPhone, iPad, and iPod touch - Apple Support