b^(n-1)/(a^n)+ a^(n-1)/(b^n)-1/a-1/b
= b^(n-1)/(a^n)+ a^(n-1)/(b^n)-a^(n-1)/(a^n)- b^(n-1)/(b^n)
=[ b^(n-1)- a^(n-1)]/ (a^n)+ [ a^(n-1)- b^(n-1)]/ (b^n)
=[ a^(n-1)- b^(n-1)] [ (a^n)-(b^n)]/(ab)^n
∵a>0,b>0,
∴a-b与a^(n-1)- b^(n-1),(a^n)-(b^n)同号,
[ a^(n-1)- b^(n-1)] [ (a^n)-(b^n)]>0,(ab)^n>0,
∴[ a^(n-1)- b^(n-1)] [ (a^n)-(b^n)]/(ab)^n
b^(n-1)/(a^n)+ a^(n-1)/(b^n)>1/a1/b