Question

已知abc=1,求1/ab+a+1+1/bc+b+1+/ac+c+1的值

Answer 1

就是将1换成abc,将分母化成一样即可

1/(ab+a+1)+1/(bc+b+1)+1/(ac+c+1)

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

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

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

=1