若abc=1，则aab+a+1+bbc+b+1+cca+c+1的值是（）A.1B.0C.-1D.-2

Question

若abc=1，则(a)/(ab+a+1)+(b)/(bc+b+1)+(c)/(ca+c+1)的值是（　　）
A. 1
B. 0
C. -1
D. -2

Answer 1

∵abc=1，∴a，b，c均不为0，则
(a)/(ab+a+1)+(b)/(bc+b+1)+(c)/(ca+c+1)
=(ac)/(1+ac+c)+(b)/(bc+b+1)+(bc)/(1+bc+b)
=(abc)/(b+1+bc)+(b)/(bc+b+1)+(bc)/(1+bc+b)
=(1+b+bc)/(b+1+bc)=1．
故选A．