Question

x^6-x^2/x^2-2x+1, x diferente de 1

Answer 1

x²-2x+1=(x-1)²

x⁶-x²=x²*(x⁴-1) =x²*(x²-1)(x²+1)=x²*(x+1)*(x-1)*(x²+1)

(x⁶-x²)/(x²-2x+1)

=x²*(x+1)*(x-1)*(x²+1)/(x-1)²

=x²*(x+1)*(x²+1)/(x-1)