if a+b=0 then (1+x^a)^-1+(1+x^b)^-1=
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(1+x^a)^-1+(1+x^b)^-1
={1+x^a+1+x^b}÷{(1+x^a)(1+x^b)}
={2+x^a+x^b}÷{1+x^a+x^b+x^(a+b)}
={2+x^a+x^b}÷{1+x^a+x^b+x^0}. [as a+b =0]
={2+x^a+x^b}÷{1+x^a+x^b+1}. [ as x^0=1]
={2+x^a+x^b}÷{2+x^a+x^b}
=1
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