1/(1 + x ^ a + x ^ b) + 1/(1 + x ^ (- a) + x ^ (b - a)) + 1/(1 + x ^ (- b) + x ^ (a - b)) = 1 proof
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Answer:
Prove-
(i)
(i)
[
x
1
a−b
]
1
a−c
⋅
[
x
1
b−c
]
1
b−a
⋅
[
x
1
c−a
]
1
c−b
=1
[x1a-b]1a-c⋅[x1b-c]1b-a⋅[x1c-a]1c-b=1
(ii)
(ii)
(
x
a−b
)
a+b
⋅
(
x
b−c
)
b+c
⋅
(
x
c−a
)
c+a
=1
(xa-b)a+b⋅(xb-c)b+c⋅(xc-a)c+a=1
<br>
(iii)
(iii)
[{
x
a(a−b)
x
a(a+b)
}÷{
x
b(b−a)
x
b(b+a)
}]
a+b
=1
[{xa(a-b)xa(a+b)}÷{xb(b-a)xb(b+a)}]a+b=1
(iv)
(iv)
(
a
x+1
a
y+1
)
x+y
⋅
(
a
y+2
a
z+2
)
y+z
⋅
(
a
- z+3
a
x+3
)
z+x
=1
(ax+1ay+1)x+y⋅(ay+2az+2)y+z⋅(az+3ax+3)z+x=1
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