Question

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

Answer 1

简单啦!abc/(ab+bc+ac)=2abc/2(ab+bc+ac)=2abc/ab+bc+ac+ab+bc+ac=2abc/a(c+b)+b(a+c)+c(a+b)

ab/(a+b)=1/3 a+b=3ab

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

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

代入

原式=2abc/(4abc+5abc+3abc)=1/6