\(M=\left(\frac{\sqrt{x}}{x-36}-\frac{\sqrt{x}-6}{x+6\sqrt{x}}\right):\frac{2\sqrt{x}-6}{x+6\sqrt{x}}\)
=\(\left(\frac{\sqrt{x}}{\left(\sqrt{x}\right)^2-6^2}-\frac{\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\right):\frac{2\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\)
=\(\left(\frac{\sqrt{x}}{\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}-\frac{\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{x-\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{x-x+6\sqrt{x}+6\sqrt{x}-36}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{12\sqrt{x}-36}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\sqrt{x}-6}\)
=\(\left(\frac{12\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-6\right)\left(\sqrt{x}+6\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}+6\right)}{2\left(\sqrt{x}-3\right)}\)
=\(\frac{6}{\sqrt{x}-6}\)