Define componendo and dividendo along with their applications in mathematics.

A theorem on proportions which is used to perform calculations and reduce the number of steps can be termed as componendo and dividendo. Some of its applications include the solving of equations involving fractions or rational functions, in mathematical olympiads. According to componendo and dividendo, if a/b = c/d , then (a+b) / (a-b) = (c+d) / (c-d).