To resolve the issue of the PBS app not opening on your TV while it works on your tablet, follow these steps:

1. Check Your Internet Connection:
- Ensure that your TV is connected to the internet. You can check this in the settings menu of your TV.

2. Power Cycle the TV:
- Unplug your TV from the power source.
- Leave it unplugged for about 1-2 minutes.
- Plug it back in and turn it on. This can often resolve temporary glitches - learn more.

3. Clear Cache and Data:
- Navigate to the settings on your TV.
- Find the option for managing applications or apps.
- Locate the PBS app and select "Clear Cache" and "Clear Data." This can help if there are corrupted files causing the app to fail - learn more.

4. Reinstall the PBS App:
- If the app still does not open, uninstall it from your TV.
- Restart your TV, then go to your app store to reinstall the PBS app. This fresh installation can eliminate any issues with the previous version - learn more.

5. Check for Updates:
- Make sure that your TV's operating system and the PBS app are both updated to their latest versions. Go to the settings and check for any software updates that might be available.

6. Network Issues:
- If using a VPN or ad-blocker, try disabling them as they can interfere with app connectivity. Reconnect to your network and attempt to launch the app again - learn more.

7. Consult PBS Help:
- If none of the above steps work, visit the PBS support website for additional troubleshooting steps or contact their customer support for more assistance - learn more.

By following these actions sequentially, you should be able to identify and resolve the issue with the PBS app on your TV.