Question

已知abc=1，求ab+a+1分之a+bc+b+1分之b+ac+c+1分之c的值

帮个忙昂
要有公式的

Answer 1

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

a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=a/(ab+a+abc)+b/(bc+b+1)+c/(ac+c+abc) 利用abc=1
=a/a(b+1+bc)+b/(bc+b+1)+c/c(a+1+ab)
=a/a(b+1+bc)+b/(bc+b+1)+c/c(a+abc+ab) 利用abc=1
=a/a(b+1+bc)+b/(bc+b+1)+c/ac(1+bc+b)
=ac/ac(b+1+bc)+abc/ac(bc+b+1)+c/ac(1+bc+b) 通分
=(ca+abc+c)/ac(1+bc+b)
=(ac+1+c)/(ac+abc*c+abc)
=(ac+1+c)/(ac+c+1)
=1