Question Number 124390 by ELIZAR last updated on 03/Dec/20
Answered by benjo_mathlover last updated on 03/Dec/20
$$\frac{\mathrm{31}}{\mathrm{9}}=\:\mathrm{3}+\frac{\mathrm{4}}{\mathrm{9}}=\:\mathrm{4}−\frac{\mathrm{5}}{\mathrm{9}}\:=\:\mathrm{4}−\frac{\mathrm{1}}{\frac{\mathrm{9}}{\mathrm{5}}}=\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{6}}{\mathrm{5}}} \\ $$$$=\:\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{1}}{\frac{\mathrm{5}}{\mathrm{6}}}}\:=\:\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{6}}}} \\ $$