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

Answer:

• B. 1

Step-by-step 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