Question

If a-b/c + b-c/a + c+a/b = 1 then show that 1/a = 1/b + 1/c

Answer 1

(a-b)/c +(b-c)/a +(c+a)/b=1

(a-b)/c +(b-c)/a +(c+a)/b=1+1-1

(a-b)/c+1 +(b-c)/a-1 +(c+a)/b-1=0

{(a-b)/c+1} +{(b-c)/a-1} +{(c+a)/b-1}=0

(a-b+c)/c +(b-c-a)/a +(c+a-b)/b=0

(a-b+c)/c -(-b+c+a)/a +(c+a-b)/b=0

(a-b+c)/c -(a-b+c)/a +(a-b+c)/b=0

(a-b+c)(1/c-1/a+1/b)=0

so {1/c-1/a+1/b}=0

=>1/a=1/b+1/c.