M:entetemax: titre="Décompositions en éléments simples" taille="1.3"


%S{Énoncé}

FICHIER:enonce.tex::
Décomposer les fractions suivantes en éléments simples dans $\R(X)$.
\everymath{\displaystyle}
\begin{multicols}{3}
  \begin{enumerate}
        \item  $\frac{X^2+1}{(X-1)(X-2)(X-3)}$
        \item  $\frac{X-2}{X^2(X-1)}$
        \item  $\frac2{X(X-1)^2}$
        \item  $\frac{X^5+X^2-X+1}{(X-1)^3}$
        \item  $\frac{3X-1}{X^2(X-1)^2}$
        \item  $\frac1{X^3+1}$
        \item  $\frac{X-2}{X^4-1}$
        \item  $\frac{X^3+2}{X^3(X^4-1)}$
        \item  $\frac1{X^4+X^2+1}$
        \item  $\frac{4X^3}{(X^4-1)^2}$
	\item  $ {{X^2+2X+5}\over{X^2-3X+2}}$
	\item  $ {{X(X^6-1)}\over{(X^2-1)^3}}$
	\item  $ {{16}\over{(X-1)^3(X+1)^3}}$
	\item  $ {1\over{(X^3+3X^2+2X)^4}}$
	\item  $ {{X^8+X+1}\over{X^4(X-1)^3}}$
	\item  $ {{X^7+1}\over{(X^2+X+1)^3}}$
	\item  $ {{X^8+1}\over{(X-1)^2(X^3-8)}}$
	\item  $ {{X^2+X+1}\over{X^3(X^2+1)^2}}$
	\item  $ {{X^2}\over {X^4-2X^2\cos\alpha+1}}$
  \end{enumerate}	
\end{multicols}
§


M:texel: f="enonce" patron="latex"

%P{}

%S{Calculs}

FICHIER:liste.txt:
>partfrac((X^2+1)/((X-1)*(X-2)*(X-3)),X);
>partfrac((X-2)/(X^2*(X-1)),X);
>partfrac(2/(X*(X-1)^2),X);
>partfrac((X^5+X^2-X+1)/(X-1)^3,X);
>partfrac(1/(X^3+1),X);
>partfrac((X-2)/(X^4-1),X);
>partfrac((X^3+2)/(X^3*(X^4-1)),X);
>partfrac(1/(X^4+X^2+1),X);
>partfrac(4*X^3/(X^4-1)^2,X);
>partfrac((X^2+2*X+5)/(X^2-3*X+2),X);
>partfrac(X*(X^6-1)/(X^2-1)^3,X);
>partfrac(16/((X-1)^3*(X+1)^3),X);
>partfrac(1/(X^3+3*X^2+2*X)^4,X);
>partfrac((X^8+X+1)/(X^4*(X-1)^3),X);
>partfrac((X^7+1)/(X^2+X+1)^3,X);
>partfrac((X^8+1)/((X-1)^2*(X^3-8)),X);
>partfrac((X^2+X+1)/(X^3*(X^2+1)^2),X);
>partfrac(X^2/(X^4 -2*X^2*cos(alpha)+1),X);
>partfrac(X^2/(X^4 -2*X^2*(2*(cos(alpha/2))^2-1)+1),X);

§

M:seq2fabA:  f="liste"

%RM{*.tmp *.log *.out *.aux *.dvi *.tex}