SOLUTION: abc=1 show that 1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)=1

Question 940411: abc=1
show that
1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)=1
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
abc=1
show that

since abc=1,   and .  Substituting





Multiply 1st fraction by  and 2nd fraction by 



All the denominators are the same



which is just 1

Edwin

RELATED QUESTIONS
prove that abc / a^-1*b^-1 + b^-1*c^-1+ c^-1*a^-1... (answered by ikleyn)

Find abc, If: a + 1/b = 7/3 b + 1/c = 4 c + 1/a =... (answered by ikleyn,Edwin McCravy,math_tutor2020)

Solve (1-a)(1-b)(1-c)... (answered by vleith)

show that... (answered by richwmiller)