∵abc=1,
∴
a
ab+a+1 +
b
bc+b+1 +
c
ca+c+1
=
abc
abbc+abc+bc +
b
bc+b+1 +
abc
caab+abc+ca
=
1
bc+b+1 +
b
bc+b+1 +
1
a+1+ab
=
1
bc+b+1 +
b
bc+b+1 +
bc
abc+bc+abbc
=
b+1
bc+b+1 +
bc
bc+b+1
=
bc+b+1
bc+b+1
=1.
∵abc=1,
∴
a
ab+a+1 +
b
bc+b+1 +
c
ca+c+1
=
abc
abbc+abc+bc +
b
bc+b+1 +
abc
caab+abc+ca
=
1
bc+b+1 +
b
bc+b+1 +
1
a+1+ab
=
1
bc+b+1 +
b
bc+b+1 +
bc
abc+bc+abbc
=
b+1
bc+b+1 +
bc
bc+b+1
=
bc+b+1
bc+b+1
=1.