Question

If abc=1 prove that 1/(1+a+b^-1) + 1/(1+b+c^-1) +1/(1+c+a^-1) =1

Answer 1

ABC=1

Explanation:

Answer 2

Answer with explanation:

It is given that, abc=1

`\rightarrow (1)/(1+a+b^(-1))+(1)/(1+b+c^(-1))+(1)/(1+c+a^(-1))\\\\\rightarrow (b)/(b+ab+1)+(c)/(c+bc+1)+(a)/(a+ac+1)\\\\abc=1\\\\\rightarrow (b)/(b+ab+abc)+(c)/(c+bc+abc)+(a)/(a+ac+abc)\\\\\rightarrow (1)/(1+a+ac)+(1)/(1+b+ab)+(1)/(1+c+bc)\\\\\rightarrow (1)/(abc+a+ac)+(1)/(1+b+ab)+(1)/(1+c+bc)\\\\\rightarrow (1+a)/(a(bc+1+c))+(c)/(c+bc+1)\\\\\rightarrow(1+a+ac)/(a(bc+1+c))\\\\\rightarrow(1+a+ac)/(abc+a+ac))\\\\\rightarrow(1+a+ac)/(1+a+ac))\\\\=1`

Hence proved.