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Question Number 43706 by Tawa1 last updated on 14/Sep/18

$$\mathrm{If}\mathrm{pqr}=1$$$$\mathrm{Hence}\mathrm{evaluate}:\frac{1}{1+\mathrm{e}+{\mathrm{f}}^{-1}}+\frac{1}{1+\mathrm{f}+{\mathrm{g}}^{-1}}+\frac{1}{1+\mathrm{g}+{\mathrm{e}}^{-1}}$$

Commented by Joel578 last updated on 14/Sep/18

$$p,q,r\mathrm{and}e,f,g?$$

Commented by Tawa1 last updated on 14/Sep/18

$$\mathrm{No}\mathrm{value}\mathrm{is}\mathrm{given}\mathrm{sir}.\mathrm{That}\mathrm{is}\mathrm{just}\mathrm{the}\mathrm{question}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 14/Sep/18

$$\frac{1}{1+p+q^{-1}}+\frac{1}{1+q+r^{-1}}+\frac{1}{1+r+p^{-1}}$$$$\frac{q}{q+pq+1}+\frac{1}{1+q+pq}+\frac{1}{1+\frac{1}{pq}+\frac{1}{p}}$$$$\frac{q}{q+pq+1}+\frac{1}{1+q+pq}+\frac{pq}{pq+1+q}$$$$=\frac{q+1+pq}{q+pq+1}=1$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Commented by Tawa1 last updated on 14/Sep/18

$$\mathrm{wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by Meritguide1234 last updated on 15/Sep/18

$$youhavesolveddifferentproblem$$

Commented by Tawa1 last updated on 14/Sep/18

$$\mathrm{I}\mathrm{understand}.\mathrm{the}\mathrm{solution}\mathrm{is}\mathrm{correct}.\mathrm{God}\mathrm{bless}\mathrm{mr}\mathrm{tanmay}$$

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