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Why do we do that?? Componendo and Dividendo is used quite often in mathematics but I cannot figure out the reason for which we do that.

Christian Blatter
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user749744
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    Actually, it is used very rarely, mostly in elementary texts. Usually people simply divide by $b$ on the left and $d$ on the right, and then replace $\frac{a}{b}$ by $\frac{c}{d}$ without invoking any special rule. – Conifold Feb 11 '20 at 05:14
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    I've never used componendo nor dividendo, and I've been doing math since the beginning of time. Are they anything like Abbott and Costello? – Gerry Myerson Feb 11 '20 at 05:38
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    Never heard of it. Is it Spanish or Italian? – Lee David Chung Lin Feb 11 '20 at 07:45
  • @GerryMyerson Using Componendo and Dividendo means substituting an equation of form $\frac ab=\frac cd$ as $\frac {a+b}{a-b}=\frac {c+d}{c-d}$ or visa-versa. – Sam Feb 11 '20 at 16:17

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Componendo-dividendo is a useful little trick used to simplify particular equations. It is quite unnecessary but it does reduce the number of steps you have to perform to get your answer. It is mostly only used when the LHS is of the form $\frac {x+a}{x-a}$ and you have to solve for $x$.

Sam
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