判断・推量N2
〜かねる、〜かねない
cannot bring oneself to... / could possibly... (negative)
Structure
V-ます形（語幹）+ かねる／かねない
Explanation
〜かねる (attached to the masu-stem) means "hard to do / cannot do", used as a polite refusal (e.g., お答えかねます). 〜かねない means "could possibly happen (something bad)", used when worrying about a negative outcome.
Examples
私の説明では、皆さんを十分に納得させかねます。
I'm afraid my explanation alone cannot fully convince everyone.
そんなに無理をすると、体を壊しかねない。
If you push yourself that hard, you could end up ruining your health.
Note
〜かねる politely expresses that one cannot do something; 〜かねない refers only to negative consequences, usually with a third-person subject.