[tex]\displaystyle\bf\\1)\\\\\frac{1}{x-4} :\frac{x+4}{4x-16}=\frac{1}{x-4} \cdot\frac{4\cdot(x-4)}{x+4} =\frac{4}{x+4}\\\\\\2)\\\\\frac{4}{x+4} +\frac{x^{2} -4x}{x^{2} -16} =\frac{4}{x+4} +\frac{x^{2} -4x}{(x+4)(x-4)} =\\\\\\=\frac{4\cdot(x-4)+x^{2} -4x}{x^{2} -16} =\frac{4x-16+x^{2} -4x}{x^{2} -16}=\frac{x^{2}-16 }{x^{2} -16} =1 \\\\x\neq -4 \ ; \ x\neq 4[/tex]