わけがない・ようがない・ようもない: the difference
わけがないN3
Meaning
There is no way, There is no reason, It is impossible, Cannot be
Past papers
Tested 2 times in past papers
Example
彼が嘘をつくわけがない。
There is no way he would lie.
Meaning
There's no way to, It's impossible to
Past papers
Tested 4 times in past papers
Example
何とも言いようがない味だ。
There is no way to put this taste/flavor into words.
How to tell them apart
「ようがない」: no means or conditions, so you can't do it even if you want to; a feeling of helplessness.
「できない」: simply cannot; could be lack of ability or a rule against it.
「わけがない」: impossible by common sense.