当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca

问题描述:

当ab/a+b=3/2,bc/b+c=3,ac/a+c=999/1000.求abc/ab+bc+ca

ab/a+b=3/2
a+b/ab=2/3
1/a+1/b=2/3
同理
1/a+1/c=1000/999
1/b+1/c=1/3
2(1/a+1/b+1/c)=1999/999
(ab+ac+bc)/abc=1999/1998
abc/ab+bc+ca=1998/1999