Ta có: \(\left(x^5+x^3+x^2+1\right):\left(x^5+1\right)\)
\(=\frac{x^3\left(x^2+1\right)+\left(x^2+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)
\(=\frac{\left(x^2+1\right)\left(x^3+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)
\(=\frac{\left(x^2+1\right)\left(x+1\right)\left(x^2-x+1\right)}{\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)}\)
\(=\frac{x^4-x^3+x^2+x^2-x+1}{x^4-x^3+x^2-x+1}\)
\(=\frac{x^4-x^3+2x^2-x+1}{x^4-x^3+x^2-x+1}\)