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Question-187903




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

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