What is the whole purpose of doing componendo and Dividendo

Question

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.

Answer 1

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 $x$.