解:过点N做NO//BC交AM于O,由题意知 BM/MC=BM/(BC-BM)=bBC/(BC-bBC)=1/(1-b) 所以ON/BM=OP/PM=(1-b)ON/MC=a(1-b) 而AO=aAM=a(AO+OM) => (1-a)AO=aOM=a(OP+PM)=a(a(1-b)PM+PM)=a(a-ab+1)PM 所以AP/PM=(AO+OP)/PM=AO/PM+OP/PM=a(a-ab+1)+a(1-b)=a²-a²b-ab+2a