已知b+1/c=1,c+1/a=1,求证(ab+1)/b=1

Question

已知b+1/c=1,c+1/a=1,求证(ab+1)/b=1

Answer 1

b+1/c=1
1/c=1-b 1
c+1/a=1
c=1-1/a 2
1式*2式得
1=(1-b)(1-1/a)=1-1/a-b+b/a
1/a+b=b/a 两边乘a
1+ab=b 两边除b
(ab+1)/b=1