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Question
Prove that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
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Solution
Consider the left hand side:
`1/(1+x^(a-b))+1/(1+x^(b-a))`
`=1/(1+x^a/x^b)+1/(1+x^b/x^a)`
`=1/((x^b+x^a)/x^b)+1/((x^a+x^b)/x^a)`
`=x^b/(x^b+x^a)+x^a/(x^a+x^b)`
`=(x^b+x^a)/(x^a+x^b)`
= 1
Therefore left hand side is equal to the right hand side. Hence proved.
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