Question Number 15788 by tawa tawa last updated on 13/Jun/17
$$\mathrm{Find}\:\mathrm{all}\:\mathrm{rational}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{ab} \\ $$
Commented by mrW1 last updated on 14/Jun/17
$$\mathrm{b}=\frac{\mathrm{n}}{\mathrm{m}} \\ $$$$\mathrm{a}+\frac{\mathrm{n}}{\mathrm{m}}=\mathrm{a}×\frac{\mathrm{n}}{\mathrm{m}} \\ $$$$\left(\frac{\mathrm{n}}{\mathrm{m}}−\mathrm{1}\right)\mathrm{a}=\frac{\mathrm{n}}{\mathrm{m}} \\ $$$$\mathrm{a}=\frac{\mathrm{n}}{\mathrm{n}−\mathrm{m}} \\ $$$$\Rightarrow\begin{cases}{\mathrm{a}=\frac{\mathrm{n}}{\mathrm{n}−\mathrm{m}}}\\{\mathrm{b}=\frac{\mathrm{n}}{\mathrm{m}}}\end{cases} \\ $$$$\mathrm{n},\mathrm{m}\in\boldsymbol{\mathrm{Z}}\wedge\mathrm{n}\neq\mathrm{m} \\ $$
Commented by tawa tawa last updated on 14/Jun/17
$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$