Question

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

除号是分数线

Answer 1

1/a+1/b=3,1/b+1/c=4,1/a+1/c=5
所以1/a+1/b+1/c=(3+4+5)/2=6
abc/（ab+bc+ca）=1/6

Answer 2

ab/（a+b）=1/3，bc/（b+c）=1/4，ac/(a+c)=1/5
(a+b)/ab=3，(b+c)/bc=4，(a+c)/ac=5
1/a+1/b=3,1/b+1/c=4,1/a+1/c=5
1/a+1/b+1/c=(3+4+5)/2=6
abc/（ab+bc+ca）=1/[（ab+bc+ca）/abc]=1/(1/c+1/a+1/b)=1/6

Answer 3

ab/（a+b）=1/3，bc/（b+c）=1/4，ac/(a+c)=1/5,
1/a+1/b=3
1/b+1/c=4
1/a+1/c=5
1/c=3,1/b=1,1/a=2
abc/（ab+bc+ca）=t
1/t=1/a+1/b+1/c=6
abc/（ab+bc+ca）=1/6