Question Number 187903 by Mingma last updated on 23/Feb/23
Answered by HeferH last updated on 23/Feb/23
Commented by HeferH last updated on 23/Feb/23
$${i}.\:\:\frac{{a}+{b}}{{c}}=\:\frac{{d}}{{e}}\:\Rightarrow\:\frac{{e}}{{d}}\:=\:\frac{{c}}{{a}+{b}} \\ $$$${ii}.\:\:\frac{{a}}{{b}}\:=\:\frac{{e}\:+\:{d}}{{d}} \\ $$$$\:\frac{{a}}{{b}}\:=\:\left(\frac{{e}}{{d}}\right)\:+\:\mathrm{1} \\ $$$$\:\frac{{a}}{{b}}\:=\:\frac{{c}}{{a}+{b}}\:+\:\mathrm{1} \\ $$$$\:{a}\left({a}\:+\:{b}\right)\:=\:{bc}\:+\:{b}\left({a}+{b}\right) \\ $$$$\:{a}^{\mathrm{2}} \:+\:{ab}\:=\:{bc}\:+\:{ab}\:+\:{b}^{\mathrm{2}} \\ $$$$\:{a}^{\mathrm{2}} =\:{b}\left({b}\:+\:{c}\right)\checkmark \\ $$
Commented by Mingma last updated on 23/Feb/23
Excellent, sir!