$\text{Terme - Additon - Subtraktion - Mulitiplikation - Division}\\ \displaystyle \frac{ 4x^5-1x^4+2x^3+x^2-1}{ x^2+1} \ \small \begin{matrix} ( 4x^5&-1x^4&+2x^3&+x^2&&-1&):( x^2 +1 )= 4x^3 -1x^2 -2x +2 \\ \,-( 4x^5&&+4x^3) \\ \hline &-1x^4&-2x^3&+x^2&&-1&\\ &-(-1x^4&&-1x^2) \\ \hline &&-2x^3&+2x^2&&-1&\\ &&-(-2x^3&&-2x) \\ \hline &&& 2x^2&+2x&-1&\\ &&&-( 2x^2&&+2) \\ \hline &&&& 2x&-3&\\ \end{matrix} \\ \normalsize \\ \\ \displaystyle \frac{ 4x^5-1x^4+2x^3+x^2-1}{ x^2+1}= 4x^3-1x^2-2x+2+\frac{ 2x-3}{ x^2+1}$