Question

已知abc=1,求a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)

Answer 1

∵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