\def{integer u=random(-5..5)}
\def{integer a=random(-5..5)}
\def{integer b=random(-5..5)}
\def{integer c=random(1,-1)*random(1..5)}

\def{text data=pari(expr=(\a)*(y+(\u))^2+(\b)*(y+(\u))+(\c);
[(\a)*x^2+(\b)*x+(\c),
x-(\u),
expr,
polcoeff(expr,2,y),
polcoeff(expr,1,y),
(\a)*(\u)^2+(\b)*(\u)+(\c),
y+(\u)])}

\def{text P= item(1,\data)}
\def{text R= item(2,\data)}
\def{text fraction= (\P)/(\R)^3}
\def{text fraction1=item(3,\data)}
\def{text fraction= (\P)/(\R)^3}
\def{text solA= item(4,\data)}
\def{text solB= item(5,\data)}
\def{text solC= item(6,\data)}
\def{text z= item(7,\data)}
<p>Considrons la fraction rationnelle 
<center>
<p>
\(\fraction)
</center>
On cherche \(A), \(B) et \(C) tels que 
<p>
<center>
\(\fraction   =  A/(\R) + B/(\R)^2+C/(\R)^2 )
</center>

On fait le changement de variables \(x = \z). On a donc
<center>\(\fraction = (\fraction1)/y^3 = \solA/y+\solB/y^2+
\solC/y^3)
</center>Donc 
<center>\(\fraction = (\solA)/(\R)+(\solB)/(\R)^2+(\solC)/(\R)^3)
</center>

\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}
