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In this paper, we establish the existence of positive solution for the semipositone second-order three-point boundary value problem $u''(t)+lambda f(t,u(t))=0$, $0<t<1$, $u(0)=alpha u(eta)$, $ u(1)=eta u(eta)$. Our arguments are based on the well-known Guo-Krasnosel'skii fixed-point theorem in cones.