～ようがない
no way to / cannot possibly
～ようがない attaches ようがない to the ます-stem of a verb. The よう here is a noun meaning “way of doing” (written 様), so 直しようがない is literally “a way of fixing does not exist”.
It expresses that the action is impossible because the speaker has no means to do it, every route is closed. English equivalents are “there's no way to ...” and “cannot possibly ...”.
No means available
The sentence usually names the missing prerequisite first, then concludes with ～ようがない.
連絡先がないので、連絡しようがない。
“I have no way to contact him, since I don't have his contact information.”
- 連絡先（れんらくさき）= contact information
- が = subject marker
- ない = there is not
- ので = because, since
- 連絡しようがない（れんらくしようがない）= have no way to get in touch
ここまで壊れていると、直しようがない。
“Broken this badly, there's no way to fix it.”
- ここまで = to this point, this far
- 壊れている（こわれている）= is broken
- と = when, if (conditional)
- 直しようがない（なおしようがない）= cannot possibly fix
Compare this with the plain potential negative ～できない: 連絡できない just states that contacting is not possible, while 連絡しようがない stresses that no method exists at all, there is nothing the speaker could even try.
How to form it
Verb ます-stem + ようがない
- 連絡する（れんらくする）= to contact → 連絡しようがない（れんらくしようがない）= no way to contact
- 直す（なおす）= to fix → 直しようがない（なおしようがない）= no way to fix
- 助ける（たすける）= to help → 助けようがない（たすけようがない）= no way to help
Key idea
～ようがない says the way itself does not exist: the action is impossible not because of ability or permission, but because there is simply no means of doing it.
Built on the same stem
Updated .