Section 003 : Componendo and Dividendo

Introduction
Componendo and Dividendo is one of the tools of mathematics related to ratio to make the calculation simpler.
Statement
if $\frac{a}{b} = \frac{c}{d}$ then $\frac{a+b}{a- b} = \frac{c+d}{c-d}$
Proof
$\frac{a}{b} = \frac{c}{d}\cdots(1) $ given
add 1 on both sides
$\frac{a+b}{b} = \frac{c+d}{d}\cdots(2) $
subtract 1 from both sides of (1) to get
  $\frac{a-b}{b} = \frac{c-d}{d}\cdots(3) $
dividing (2) by (3) we get
$\frac{a+b}{a- b} = \frac{c+d}{c-d}$
Usefulness
This is useful to speed up the mathematical calculations as specified in example below
example example 1