\(=\frac{x-12}{6\left(x-6\right)}-\frac{6}{x\left(x-6\right)}\)
\(=\frac{x^2-12x-36}{6x\left(x-6\right)}\)
\(=\frac{\left(x-6-6\sqrt{2}\right)\left(x-6+6\sqrt{2}\right)}{6x\left(x-6\right)}\)
\(\frac{x-12}{6x-36}-\frac{6}{x^2-6x}=\frac{\left(x-12\right)\left(x^2-6x\right)}{\left(6x-36\right)\left(x^2-6x\right)}-\frac{6\left(6x-36\right)}{\left(x^2-6x\right)\left(6x-36\right)}\)
\(=\frac{x^3-6x^2-12x^2+72x}{\left(6x-36\right)\left(x^2-6x\right)}-\frac{36x-216}{\left(x^2-6x\right)\left(6x-36\right)}\)
\(=\frac{x^3-18x^2+72x-36x+216}{\left(6x-36\right)\left(x^2-6x\right)}=\frac{x^3-18x^2+36x+216}{\left(6x-36\right)\left(x^2-6x\right)}\)
