Verified answer

[tex]\displaystyle \frac{2m}{m^2-6m+9}-\frac{6}{m-3}=\frac{2m}{(m-3)^2}-\frac{6}{m-3}=\frac{2m-6(m-3)}{(m-3)^2}=\frac{2m-6m+18}{(m-3)^2}=\\\\\frac{18-4m}{(m-3)^2}[/tex]