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Mobile-edge computing (MEC) is an emerging paradigm that provides a capillary distribution of cloud computing capabilities to the edge of the wireless access network, enabling rich services and applications in close proximity to the end users. In this paper, an MEC enabled multi-cell wireless network is considered where each base station (BS) is equipped with a MEC server that assists mobile users in executing computation-intensive tasks via task offloading. The problem of joint task offloading and resource allocation is studied in order to maximize the users' task offloading gains, which is measured by a weighted sum of reductions in task completion time and energy consumption. The considered problem is formulated as a mixed integer nonlinear program (MINLP) that involves jointly optimizing the task offloading decision, uplink transmission power of mobile users, and computing resource allocation at the MEC servers. Due to the combinatorial nature of this problem, solving for optimal solution is difficult and impractical for a large-scale network. To overcome this drawback, we propose to decompose the original problem into a resource allocation (RA) problem with fixed task offloading decision and a task offloading (TO) problem that optimizes the optimal-value function corresponding to the RA problem. We address the RA problem using convex and quasi-convex optimization techniques, and propose a novel heuristic algorithm to the TO problem that achieves a suboptimal solution in polynomial time. Simulation results show that our algorithm performs closely to the optimal solution and that it significantly improves the users' offloading utility over traditional approaches.