What is the concept of componendo and divendo?

If a:b::c:d (i,e the ratio that a bears to b is the same as the ratio that c bears to d),then (a+b):(a-b)::(c+d)(c-d). (the ratio of a+b to a-b is same as the ratio that c+d bears to c-d)

Writing in algebraic form: If  

 

This property is frequently used in simplification.