Question

已知ab/a+b=1/3 bc/a+c=1/4 ac/a+c=1/5 求abc/ab+ac+bc

Answer 1

因为ab/(a+b）=1/3,bc/(a+c）=1/4 ,ac/(a+c）=1/5

所以1/a+1/b=b/ab+a/ab=(a+b)/ab=3

1/b+1/c=c/bc+b/bc=(c+b)/bc=4

1/a+1/c=c/ac+a/ac=(c+a)/ac=5

三式两边相加就有

2(1/c+1/b+1/a)=3+4+5=12

又因为(ab+ac+bc )/abc

=1/c+1/b+1/a=6

所以abc/(ab+ac+bc)=1/6