Our task is to simplify expressions of the form

by expressing them in the form

or

To express in terms of the first, we write,

Remembering now that are all constants, we can equate the coefficients of and on both sides, to give simultaneous equations:

For (1) and (2)

(2)/(1) givesand

so where and are given as above.

A similar procedure gives, when we want to write,as

Example:

Write in the form

and

We may also be asked to solve equations such as As above, we write and put this equal to 1. We solve