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