已知：abc=1,试说明1/(ab+a+1)+1/(bc+b+1)+1/(ac+c+1)=1

来源：学生作业学帮网编辑：学帮网时间：2024/05/27 14:25:08

证明：[1/(ab+a+1)]+[1/(bc+b+1)]+[1/(ac+c+1)] =[1/（ab+a+abc)]+[1/(bc+b+1)]+[1/(ac+c+abc)] =[1/a(b+1+bc)]+[1/(b+1+bc)]+[1/c(a+1+ab)] =[1/a(b+1+bc)]+[1/(b+1+bc)]+[1/ac(b+1+bc)] =1/(b+1+bc)*[(1/a)+1+(1/ac)] =1/(b+1+bc)*[bc+1+b] =1