Question

已知abc=1，求a/(ab+a+1）+b/(bc+b+1)+c/(ac+c+1）的值(麻烦用文字叙述）

Answer 1

a/(ab+a+1）=ac/(abc+ac+c)=ac/(ac+c+1)
b/(bc+b+1)=abc/(abc²+abc+ac)=1/(c+1+ac)
a/(ab+a+1）+b/(bc+b+1)+c/(ac+c+1）
=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1

Answer 2

因为abc=1.
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=a/(ab+a+1)+ab/(abc+ab+a)+abc/(abac+abc+ab)
=a/(ab+a+1)+ab/(1+ab+a)+1/(a+1+ab)
=(ab+a+1)/(ab+a+1)
=1

Answer 3

.