1-1-x-b-a-x -a-1-1-xa-b-x - c-b-1-1-x-b-c-xa-c-

The correct option is A 1 [ Given exp = 1/( 1 + x^b/x^a + x^c/x^a) + 1/( 1 + x^a/x^b + x^c/x^b) + 1/( 1 + x^b/x^c + x^a/x^c); = x^a/( x^ ...

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Second Fundamental Theorem of Calculus

1/1+x[b-a+x |...

Question

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

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x ^{a – b – c}

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x^abc

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y = \frac{a x^{2}}{(x - a) (x - b) (x - c)} + \frac{b x}{(x - b) (x - c)} + \frac{c}{x - c} + 1,

\frac{y^{'}}{y}

(Here, y^{'} = \frac{d y}{d x})

x, y, z

a, b, c

\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}}

x, y, z

a, b, c

\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}}

\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)}} = ?

Prove that:

(i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

(ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

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