The　aim　of　this　paper　is　to　discuss　the　fractional　programming　problem　(P)　that　an　objective　function　is　a　ratio　of　two　DC　(difference　of　convex)　functions　with　finitely　many　DC　constraints.　A　type　of　dual　problem　is　constructed　and　the　duality　assertions　are　obtained.　By　using　the　obtained　duality　assertions,　some　Farkas-type　results　which　characterize　the　optimal　value　of　the　problem　(P)　are　given.　Some　programming　problems　considered　in　recent　literature　are　the　special　cases　of　the　problem　(P).　(C)　2010　Elsevier　Ltd.　All　rights　reserved.