Question
If abc = 1. then `((1)/(1 + a + b^-1) + (1)/(1 + b + c^-1) + (1)/(1 + c + a^-1))` = ?.
Answer: Option B
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Given Exp. `(1)/(1 + a + b^-1) + (1)/(1 + b + c^-1) + (1)/(1 + c + a^-1)`
= `(1)/(1 + a + b^-1) + (b^-1)/(b^-1+1 + b^-1 c^-1) + (a)/(a + ac + 1)`
= `(1)/(1 + a + b^-1) + (b^-1)/(1 + b^-1 + a) + (a)/(a + b^-1 + 1)`
=`(1 + a + b^-1)/(1 + a + b^-1)` = 1.
[ `:.` abc = 1 `rArr` `(bc)^-1` = a `rArr` `b^-1 c^-1` = a and ac = `b^-1` ]
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