One side of the screen's hinge broke on my UX303UB. Can it be fixed?

You can definitely fix it without buying a complete screen assembly. First thing to do is figure out exactly what's wrong with the hinge; there are usually two different failures I've seen; first, the screws that hold the screen to the top cover can get broken or stripped out, or the reinforcing arm the runs up the side of the cover can break off. In the first instance you'd want to repair or replace the display cover, and in the second you'd replace the hinge. Here's a video showing a guy with the first problem who went to the trouble of actually repairing the broken plastic, allowing the hinge mounts to once again hold securely to the lid.

Asus UX303L - Repairing a broken hinges [4K - YouTube]

I'm all for repairing something rather than replacing it, but my main criticism of this video is that you better never plan on removing those hinges! He had the plastic piece the hinge mounts to break off completely on the left side, and the screw holes were stripped on the right side. In both cases he used two part epoxy to glue down the broken piece and fill the stripped screw holes. Afterward, he went over and added more epoxy around the edge of the hinge to further secure it to the lid. It looks like this should be a suitable fix, as long as you never have to take those hinges off again for any reason.

This second video shows what I would probably do myself, which is to buy a replacement top cover. The cover is only held onto the LCD with clips, so you can basically just pry it off once you have it separated from the keyboard.

LFC#137 - Asus UX303L Hinge Repair - YouTube

Both of these videos show a UX303L rather than a UX303U, but I compared the video to the iFixit guide and I can't see any difference in the process.

Asus ZenBook UX303U Screen Assembly Replacement - iFixit Repair Guide

The second video also has suggestions for finding that cover; they suggest two of my usual sources, eBay and AliExpress, but there's always Amazon as well. A general internet search may turn up other suppliers as well, so find one that suits you.

As you work, take lots of pictures and once you're done you can piggyback onto the screen assembly guide to create your own hinge/top cover replacement guide! It's easy, fun and will have the appreciation of the repair community - and anyone who comes along after you with those same broken hinges!

Create a new Guide - iFixit

Good luck, and be sure to come on back and let us know how it all turns out for you.