Question

prove that: 1/1+x^a-b + 1/1+x^b-a=1

Answer 1

lets assume 1+x^a-b=t
x^a-b=t-1,
similarly, x^b-a=1/(t-1)
now put value of x^a-b and x^b-a in given equation
1/(1+t-1) +1/(1+1/(t-1))
after solving this you will get 1

Answer 2

1/(1+x^(a-b))+ 1/(1+x^(b-a))

= 1/(1+x^(a-b)) + 1/(1+x^-(a-b))

=1/(1+x^(a-b)) + (x^(a-b))/(1+x^(a-b))

=(1+x^(a-b))/(1+x^(a-b))

=1



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