[tex](\frac{2}{x-2}-\frac{3}{x+3})\cdot \frac{5x(x+3)}{12-x}-\frac{8}{x-2}+\frac{81}{x^2-4}\cdot \frac{x+2}{9}=\\
\\
\frac{2(x+3)-3(x-2)}{(x+3)(x-2)}\cdot \frac{5x(x+3)}{12-x}-\frac{8}{x-2}+\frac{9(x+2)}{(x-2)(x+2)}=\\
\\
\frac{2x+6-3x+6}{x-2}\cdot \frac{5x}{12-x}-\frac{8}{x-2}+\frac{9}{x-2}=\\
\\
\frac{12-x}{x-2}\cdot \frac{5x}{12-x}+\frac{1}{x-2}=\\
\\
\frac{5x}{x-2}+\frac{1}{x-2}=\boxed{\boxed{\boxed{\frac{5x+1}{x-2}}}}[/tex]
