Răspuns
x+1
Explicație pas cu pas:
(xⁿ+2xⁿ⁻¹+2xⁿ⁻²+...+2x²+2x+1)/(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1)=
(xⁿ+2xⁿ⁻¹+2xⁿ⁻²+...+2x²+2x+2-1)/(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1)=
(xⁿ-1)/(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) + (2xⁿ⁻¹+2xⁿ⁻²+...+2x²+2x+2)/(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) =
(x-1)(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) / (xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) +2(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) /(xⁿ⁻¹+xⁿ⁻²+...+x²+x+1) =x-1+2= x+1
