Question Number 104539 by Anindita last updated on 22/Jul/20
$$ \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}}}} \\ $$
Answered by OlafThorendsen last updated on 22/Jul/20
$$=\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}} \\ $$$$=\:\mathrm{1}−\frac{\mathrm{3}}{\mathrm{2}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$