Coherent sheaf on reduced scheme is free on dense open set

Question

It should be well-known fact, but I couldn't find this in Hartshorne's "Algebraic Geometry", Mumford-Oda or Ravi Vakil's Lecture notes. Let $X$ be a reduced connected scheme and $\mathcal F$ is a coherent sheaf on it. I want to prove that there is a dense open set $U \subset X$ such that $\mathcal F|_{U}$ is a free sheaf.