〜かねる

Meaning

Indicates that, though one wishes to, circumstances or position make it difficult to do. A formal expression for politely conveying something hard to refuse outright. Attaches to the masu-stem of verbs.

Examples

申し訳ございませんが、その件についてはお答えしかねます。 I am sorry, but I am unable to answer that question.
あまりに突然の話で、すぐには決めかねている。 It was such a sudden request that I am having difficulty deciding right away.