Question

On simplification, 1/(1+a^m-n+a^mp) + 1/(1+a^n-m+a^n-p) + 1/(1+a^p-m+a^p-n) is equal to​

Answer 1

Answer:

For clarity, each term is considered individually.

T1=11+am−n+am−p=11+aman+amap

⟹T1=an+pan+p+am+p+am+n

T2=11+an−m+an−p=11+anam+anap

⟹T2=am+pam+p+an+p+an+m

T3=11+ap−m+ap−n=11+apam+apan

⟹T3=am+nam+n+ap+n+ap+m

T1+T2+T3=11+am−n+am−p+11+an−m+an−p+11+ap−m+ap−n

=an+pan+p+am+p+am+n+am+pam+p+an+p+an+m+am+nam+n+ap+n+ap+m

=am+n+ap+n+ap+mam+n+ap+n+ap+m

=1

Ans: 1