[tex]\text{Fie a,b,c cele trei parti:}\\
\{a,b,c\} i.p.\{3;4;6\}\Rightarrow \dfrac{a}{\frac{1}{3}}=\dfrac{b}{\frac{1}{4}}=\dfrac{c}{\frac{1}{6}}=k\Rightarrow a=\dfrac{k}{3},b=\dfrac{k}{4},c=\dfrac{k}{6}\\
a+b+c=9\\
\dfrac{k}{3}+\dfrac{k}{4}+\dfrac{k}{6}=9 |\cdot 12\\
4k+3k+2k=9\cdot 12\\
9k=9\cdot 12 \Rightarrow \boxed{k=12}\\
a=\dfrac{k}{3}\Rightarrow \boxed{a=4}\\
b=\dfrac{k}{4}\Rightarrow \boxed{b=3}\\
c=\dfrac{k}{6}\Rightarrow \boxed{c=2}[/tex]
