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eduard
3 years ago
6

Plss answer!! MERRY Christmas!!! Critical Question. AAAAA​

Mathematics
1 answer:
liberstina [14]3 years ago
5 0

Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1

We take left hand side of the given equation and solve it,

\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}

Since, abc = 1,

\frac{1}{c}=ab and c = \frac{1}{ab}

By substituting these values in the expression,

\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}

                                       =\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}

                                       =\frac{1+b+ab}{1+b+ab}

                                       =1

Which equal to the right hand side of the equation.

Hence, \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1

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