Question:
show that 1/(1+x)^a_b+1/(1+x)^b_a=1
Answer:
Correct Question is:
Show that 1/(1 + xa-b ) + 1/(1 + xb-a ) = 1
Solution:
Given, 1/(1 + xa-b ) + 1/(1 + xb-a )
= 1/(1 + xa-b ) + 1/(1 + x-(a-b )
= 1/(1 + xa-b ) + 1/(1 + 1/xa-b )
= 1/(1 + xa-b ) + 1/{(xa-b + 1)/xa-b }
= 1/(1 + xa-b ) + xa-b/(xa-b + 1)
= 1/(1 + xa-b ) + xa-b /(1 + xa-b )
= (1 + xa-b )/(1 + xa-b )
= 1
So, 1/(1 + xa-b ) + 1/(1 + xb-a ) = 1
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