若 b+1/c=1,c+1/a=1,求 ab+1/b 的值.）

(1)
b+1/c=1
b=1-1/c=(c-1)/c
1/b=c/(c-1)
c+1/a=1
1/a=1-c
a=1/(1-c)
(ab+1)/b
=a+1/b
=1/(1-c)+c/(c-1)
=1/(1-c)-c/(1-c)
=(1-c)/(1-c)
=1
(2)
1/(a+b)=1/a+1/b=(a+b)/(ab)
ab=(a+b)^2=a^2+2ab+b^2
a^2+b^2=-ab
b/a+a/b
=(a^2+b^2)/ab
=-ab/ab
=-1