x^3n/(x^n-1)-x^2n/(x^n+1)-1/(x^n-1)+1/(x^n+1)
=(x³ⁿ-1)/(xⁿ-1)-(x²ⁿ-1)/(xⁿ+1)
=(xⁿ-1)(x²ⁿ+xⁿ+1)/(xⁿ-1)-(xⁿ-1)(xⁿ+1)/(xⁿ+1)
=x²ⁿ+xⁿ+1-xⁿ+1
=x²ⁿ+2