Arienna

In many of my math classes and when doing proofs and derivations of formulas for my engineering problems, you will often see a textbook noting a step called, "Multiply by a well-chosen one". This means you can multiply something by a ratio that equals one, but has a funky form to give your function a form that's easier to manipulate or simplify. If there's a trick to seeing exactly what well-chosen one you ought to use, I've never learned it. Anytime a piece of my work has been cleverly rearranged in this manner you can assume divine intervention (Or, you know, mathematics software).