The knowledge tracing task is designed to track changes of students' knowledge in real time based on their historical learning behaviors and to predict their future performance in learning. In the learning process, learning behaviors are intertwined with forgetting behaviors, and students' forgetting behaviors have a great impact on knowledge tracing. In order to accurately model the learning and forgetting behaviors in knowledge tracing, a deep knowledge tracing model LFKT (learning and forgetting behavior modeling for knowledge tracing) that combines learning and forgetting behaviors is proposed in this study. To model such two behaviors, the LFKT model takes into account four factors that affect knowledge forgetting, including the interval between students' repeated learning of knowledge points, the number of repeated learning of knowledge points, the interval between sequential learning, and the understanding degree of knowledge points. The model uses a deep neural network to predict knowledge status with indirect feedbacks on students' understanding of knowledge according to students' answers. With the experiments on the real datasets of online education, LFKT shows better performance of knowledge tracing and prediction in comparison with the traditional approaches.