a^n+2-a^2b^n/a^2n+1-ab^2n
=(a^n*a^2-a^2*b^n)/(a^2n*a-ab^2n)
=a^2(a^n-b^n)/a(a^2n-b^2n)
=a^2(a^n-b^n)/a(a^n+b^n)(a^n-b^n)
=a/(a^n+b^n)
注：【a^2n-b^2n=(a^n)^2-(b^n)^2]