Question

紧急!一道初二分式计算题 已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(c/ac+c+1)的值．

Answer 1

已知abc=1.求a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)的值.

原式= a/(ab+a+abc)+b/(bc+b+1)+c/(ac+c+1)

=1/(b+1+bc)+b/(bc+b+1)+c/(ac+c+1)········ ·分子分母约去a

=(1+b)/(b+1+bc)+c/(ac+c+1) ············前两项相加

=(1+b)/(b+1+bc)+c/(ac+c+abc) ···········后一项括号中的1换成abc；

=(1+b)/(b+1+bc)+1/(a+1+ab) ············约去c

=(1+b)/(b+1+bc)+abc/(a+abc+ab) ··········约去a

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

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

=1

其实这就是把1不停的换,换成分母相同的再加