\def{integer uu=random(1..5)}
\def{integer u=random(1,-1)*\uu}
\def{integer vv=random(\uu+1..8)}
\def{integer v=random(1,-1)*\vv}
\def{integer w=random(1,-1)*random(\vv+1..12)}
\def{integer c=random(-12..12)}
\def{integer b=random(1,-1)*random(1..12)}
\def{integer a=random(-5..5)}
\def{text data=pari(print(
(\a)*x^2+(\b)*x+(\c)","x - (\u)","x - (\v)","x - (\w)","
((\a)*(\u)^2+(\b)*(\u)+(\c))/(((\u)-(\v))*((\u)-(\w)))",
"((\a)*(\v)^2+(\b)*(\v)+(\c))/(((\v)-(\u))*((\v)-(\w)))",
"((\a)*(\w)^2+(\b)*(\w)+(\c))/(((\w)-(\u))*((\w)-(\v)))))}

\def{text P=item(1,\data)}
\def{text R1=item(2,\data)}
\def{text R2=item(3,\data)}
\def{text R3=item(4,\data)}
\def{text solA= item(5,\data)}
\def{text solB= item(6,\data)}
\def{text solC= item(7,\data)}
\def{text fraction=(\P)/((\R1)*(\R2)*(\R3))}
\def{text fraction1=(\P)/((\R2)*(\R3))}
\def{text fraction2=(\P)/((\R1)*(\R3))}
\def{text fraction3=(\P)/((\R1)*(\R2))}
Considrons la fraction rationnelle 
<center>
<p>
\(\fraction)
</center>
On cherche \(A), \(B) et \(C) tels que 
<p>
<center>
\(\fraction   =  A/(\R1) + B/(\R2) +C/(\R3))
</center>
<ul>
<li>
Pour calculer \(A),  on multiple \(\fraction) par \(\R1), on obtient 
donc \( \fraction1) et on prend la valeur en x=\u, donc 
A= \(\solA). </li>
<li>
Pour calculer \(B),  on multiple \(\fraction) par \(\R2), on obtient 
donc \( \fraction2) et on prend la valeur en x=\v, donc 
B= \(\solB). 
</li>
<li>
Pour calculer \(C),  on multiple \(\fraction) par \(\R3), on obtient 
donc \( \fraction3) et on prend la valeur en x=\w, donc 
C= \(\solC). 
</li>
</ul>
Donc
<p><center> \(\fraction   =  \solA/(\R1) + \solB/(\R2)+\solC/(\R3) )
</center>

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