Large language models (LLMs) have remarkable capabilities, but adapting them to specialized domains poses a fundamental question: how should accumulated experience be represented and leveraged? Existing approaches represent experience either as explicit textual artifacts in prompts (e.g., retrieved documents or dialogues) or implicitly within model weights via fine-tuning (e.g., LoRA adapters). However, textual methods are limited by context windows and cannot internalize knowledge, while parametric fine-tuning yields one adapter per task with minimal cross-task skill reuse. We propose ReX (Reusable eXperience), an experience-centric adaptation framework that treats latent experiences — recurring reasoning patterns and skills — as fundamental units for LLM specialization. Our method learns a shared Experience Bank of foundational skill vectors and uses a VAE-based encoder to map each input to a low-dimensional experience code. An Experience Router then dynamically composes the relevant skill vectors from this bank into a lightweight adapter for that input. By reusing skills across inputs, ReX enables implicit knowledge sharing across tasks without any explicit task identifiers. Experiments on multi-task NLP benchmarks show that this approach outperforms standard task-specific fine-tuning, yielding improved generalization through flexible skill reuse. Code is available at https://github.com/iLearn-Lab/ACL26-ReX.