Bài giải:

ĐKXĐ: x $\ne $6; x $\ne $-6; x $\ne $0; x$\ne $3

A = $\left( \frac{x}{{{x}^{2}}-36}-\frac{x-6}{{{x}^{2}}+6x} \right):\frac{2x-6}{{{x}^{2}}+6x}+\frac{x}{6-x}$

A = $\left( \frac{x}{(x-6)(x+6)}-\frac{x-6}{x(x+6)} \right):\frac{2x-6}{x(x+6)}-\frac{x}{x-6}$

A = $\frac{{{x}^{2}}-{{(x-6)}^{2}}}{x(x-6)(x+6)}:\frac{2(x-3)}{x(x+6)}-\frac{x}{x-6}$

A = $\frac{12(x-3)}{x(x-6)(x+6)}.\frac{x(x+6)}{2(x-3)}-\frac{x}{x-6}$

A = $\frac{6}{x-6}-\frac{x}{x-6}$ = -1

Vậy giá trị của biểu thức A là: -1