[tex]\displaystyle\bf\\\frac{4+x}{x^{2} +9-6x} :\frac{x^{2}-16 }{2x-6} -\frac{2}{x-4} =\frac{4+x}{x^{2} -6x+9}\cdot\frac{2x-6}{x^{2} -16} -\frac{2}{x-4} =\\\\\\=\frac{4+x}{(x-3)^{2} }\cdot\frac{2\cdot(x-3)}{(x -4)\cdot(x+4)} -\frac{2}{x-4}=\\\\\\=\frac{2}{(x-3)\cdot(x-4)} -\frac{2}{x-4} =\frac{2-2\cdot(x-3)}{(x-3)(x-4)} =\\\\\\=\frac{2-2x+6}{(x-3)(x-4)} =\frac{8-2x}{(x-3)(x-4)}=\frac{2\cdot(4-x)}{(x-3)(x-4)} =\frac{2}{3-x} \\\\\\\frac{2}{3-x}=\frac{2}{3-x}[/tex]

Тождество доказано