[tex]\dfrac{2y}{y^2-9y+18}-\dfrac{1}{y-6}=\\
\dfrac{2y}{y^2-3y-6y+18}-\dfrac{1}{y-6}=\\
\dfrac{2y}{y(y-3)-6(y-3)}-\dfrac{1}{y-6}=\\
\dfrac{2y}{(y-6)(y-3)}-\dfrac{1}{y-6}=\\
\dfrac{2y}{(y-6)(y-3)}-\dfrac{y-3}{(y-6)(y-3)}=\\
\dfrac{2y-y+3}{(y-6)(y-3)}=\\
\dfrac{y+3}{(y-6)(y-3)}[/tex]
