A couple of recommendations to proceed: CF-Auto-Root has not yet been updated, so that the installation will be more manual.
These are the four steps to enable root in the new HTC Nexus 9:
2. Fastboot oem unlock
3. Fastboot boot inject.img
4. Fastboot flash boot patched.img
Some applications will root problems because they have not yet been updated to Android 5.0 and 64 bits, but we are in the early days and is normal.
No more I leave the link to Chainfire and XDA so you can keep all the author's comments, news and any errors that may appear. If any of you already have a Nexus 9 and doubt, we can try to answer you questions here.
Update: Chainfire has released a new version of CF-Auto-Root for the Nexus root 9 that includes a new file system to work with other devices too. The link set up has now been updated with this new CF-Auto-Root. Much easier, where it will stop.