Question~ \frac{1}{1 + x {}^((b - a) ) + x {}^((c - a)) } + \frac{1}{1 + x {}^((a - b)) + {x}^((c - b)) } + \frac{1}{1 + {x}^((b - c)) + x {}^((a - c) ) } = ? A.0 B.1 C.x^(a-b-c…

Question

Question~


`\frac{1}{1 + x {}^((b - a) ) + x {}^((c - a)) } + \frac{1}{1 + x {}^((a - b)) + {x}^((c - b)) } + \frac{1}{1 + {x}^((b - c)) + x {}^((a - c) ) } = ?`

`A.0`

`B.1`

`C.x^(a-b-c)`

`D.None \: of \: these`
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Thanks for answering~~~~~~~~~~~~~~~~​

Answer 1

• B. 1

Explanation:

Multiply the first term by
`x^a`, the second term by
`x^b`, the third term by
`x^c`.

The first term becomes:

• 
  `x^a/(x^a+x^b+x^c)`

The second term becomes:

• 
  `x^b/(x^a+x^b+x^c)`

The third term becomes:

• 
  `x^c/(x^a+x^b+x^c)`

Their sum is:

• 
  `(x^a+x^b+x^c)/(x^a+x^b+x^c) = 1`

Correct choice is B