1) $$5x^{-1}-6=0$$ $$5x^{-1} = 6$$ $$\frac{5}{x} = 6$$ $$x = \frac{5}{6}$$
2) $$3 + 10x^{-1} = 0$$ $$10x^{-1} = -3$$ $$\frac{10}{x} = -3$$ $$x = \frac{10}{-3} = -\frac{10}{3}$$
3) $$(5-x^{-1})^{-1} = 2^{-2}$$ $$\frac{1}{5 - x^{-1}} = \frac{1}{2^2}$$ $$5 - x^{-1} = 4$$ $$x^{-1} = 1$$ $$\frac{1}{x} = 1$$ $$x = 1$$