With practical code reuse, the code fragments from developers' forums often migrate to applications. Owing to the incomplete nature of such fragments, they often lack the details on exception handling. The adaptation for exception handling to the codebase is not trivial as developers must learn and memorize what API methods could cause exceptions and what exceptions need to be handled. We propose Neurex, an exception handling recommender that learns from complete code, and accepts a given Java code snippet and recommends 1) if a try-catch block is needed, 2) what statements need to be placed in a try block, and 3) what exception types need to be caught in the catch clause. Inspired by the sequence chunking techniques in natural language processing, we design Neurex via a multi-tasking model with the fine-tuning of the large language model CodeBERT for these three exception handling recommendation tasks. Via the large language model, Neurex can learn the surrounding context, leading to better learning the dependencies among the API elements, and the relations between the statements and the corresponding exception types needed to be handled.