Experience is gained over a long period of practical participation or observation this in its self can enable you to become an expert. Expertise is to put your experience into practise, demonstrating your knowledge or practical ability in any given field.
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Experience comes with being there for a long time. Expertise is the special quality of being very good at a particular thing or job, could be technical or non-technical and could be more than one. With experience, you can achieve, expertise. But with expertise alone, you cannot gain experience with which goes the indepth knowledge, ability to respond to situations, wisdom, how to react to people oriented situations etc. THIS IN SHORT