$$\frac{tg75^\circ}{1-tg^275^\circ}=\frac{1}{2}\cdot\frac{2tg75^\circ}{1-tg^275^\circ}=\frac{1}{2}tg(2\cdot75^\circ)=\frac{1}{2}tg150^\circ=\frac{1}{2}tg(180^\circ-30^\circ)=-\frac{1}{2}tg30^\circ=-\frac{\sqrt{3}}{6}$$.
Ответ:$$-\frac{\sqrt{3}}{6}$$