已知1/a+1/b=3,1/b+1/c=4,1/c+1/a=5,求abc/ab+bc+ca的值

1/a+1/b=31/a=3-1/b 代入 1/c+1/a=5得1/c+3-1/b=51/c-1/b=2 11/b+1/c=4 21+2得2/c=61/c=3 c=1/32-1得2/b=21/b=1 b=1 代入1/a+1/b=3得1/a=3-1=2a=1/2abc=1/2*1*1/3=1/6ab+bc+ca=1/2*1+1*1/3+1/2*1/3=1所以abc/ab+bc+ca=1/6/1=1/6