Question

求解一道数学题，要过程

设abc等于1，求a/ab+a+1 + b/bc+b+1 +
c/ac+c+1

Answer 1

abc=1
所以
b=1/ac
ab=1/c
bc=1/a

所以原式=a/(1/c+a+1)+(1/ac)/(1/a+1/ac+1)+c/(ac+c+1)
第一个式子分子分母同乘以c
第二个式子分子分母同乘以ac
=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1

Answer 2

设abc等于1，求a/ab+a+1 + b/bc+b+1 +
c/ac+c+1
解：a/ab+a+1 + b/bc+b+1 + c/ac+c+1
＝a/ab+a+abc + b/bc+b+1 + c/(1/b)+c+1
=1/bc+b+1 + b/bc+b+1 + bc/bc+b+1
=(1+b+bc)/(1+b+bc)
=1