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Question Number 163014 by MathsFan last updated on 03/Jan/22
given (a/b)=(c/d), find an expression  for  (a/(a+b))
$${given}\:\frac{{a}}{{b}}=\frac{{c}}{{d}},\:{find}\:{an}\:{expression} \\ $$$${for}\:\:\frac{{a}}{{a}+{b}} \\ $$
Answered by som(math1967) last updated on 03/Jan/22
(b/a)+1=(d/c)+1  ((a+b)/a)=((c+d)/c)  ∴(a/(a+b))=(c/(c+d))
$$\frac{{b}}{{a}}+\mathrm{1}=\frac{{d}}{{c}}+\mathrm{1} \\ $$$$\frac{{a}+{b}}{{a}}=\frac{{c}+{d}}{{c}} \\ $$$$\therefore\frac{{a}}{{a}+{b}}=\frac{{c}}{{c}+{d}} \\ $$$$ \\ $$
Commented by MathsFan last updated on 04/Jan/22
thank you sir
$${thank}\:{you}\:{sir} \\ $$
Answered by Rasheed.Sindhi last updated on 03/Jan/22
(a/b)=(c/d)⇒b=((ad)/c)  (a/(a+b))=(a/(a+((ad)/c)))=(a/(a(1+(d/c))))=(1/((c+d)/c))=(c/(c+d))
$$\frac{{a}}{{b}}=\frac{{c}}{{d}}\Rightarrow{b}=\frac{{ad}}{{c}} \\ $$$$\frac{{a}}{{a}+{b}}=\frac{{a}}{{a}+\frac{{ad}}{{c}}}=\frac{\cancel{{a}}}{\cancel{{a}}\left(\mathrm{1}+\frac{{d}}{{c}}\right)}=\frac{\mathrm{1}}{\frac{{c}+{d}}{{c}}}=\frac{{c}}{{c}+{d}} \\ $$
Commented by MathsFan last updated on 04/Jan/22
merci
$${merci} \\ $$

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