Many of my students seem to be impressed with my method of doing partial fractions, and after I explain to them, I think they all can conclude that it is nothing more than kindergarten math tricks.

There isn’t a name to this method of doing partial fraction per se, so let us call it “plus minus zero”! The trick is to understand that what follows after every polynomial of normal is a mere plus minus zero. so we can go ahead and do whatever we want to it; be it, “+2x – 2x” or “+2-2”. And after you learn how to see what to choose to plus and minus it, everything really boils down to some really straightforward cancellation

For example, when I see things like $\frac{x}{x+2}$, I will think of introducing $-2+2$. So we have $\frac{x+2-2}{x+2} = \frac{x+2}{x+2} - \frac{2}{x+2} = 1 - \frac{2}{x+2}$

Or when we have $\frac{x^{2}}{x+1}$, I will think of $-1+1$. Then $\frac{x^{2}-1+1}{x+1} = \frac{(x+1)(x-1)}{x+1} + \frac{1}{x+1} = x - 1 + \frac{1}{x+1}$

This is a really neat and good technique to long division method, cos I don’t like to do it haha. But this takes some skills, as most students will agree. But most of my J2s are so used to seeing me do it, that they have developed this skill too. 🙂