Could it be true? An easier way to do partial fractions? This has to be the most tedious thing that you learn in all of Calculus. Well, I’m here to tell you that you should dread it no longer! No more boring systems of equations!
It is too easy to make a mistake with the traditional method of partial fractions. Although solving a system of equations is a topic covered way back in algebra, nobody ever truly masters it. Why is that? Because you fall asleep half way through the problem! You end up not paying attention fully, and making a simple error somewhere along the way. You are probably thinking, “Mike, just tell us already!” So I will!
Conventional partial fractions are done as follows:
Ughhh… that was so tedious!! Please let me show you the faster way now! Let’s look at the same problem from the beginning.
At this point, let’s take a step back and think about the equation in front of us. The constants, A, B & C, have to make this true for ANY value of x. x could be absolutely anything, and this will always be true. So, why not choose the values of x? Pick the ones that would make this problem a lot easier for us.
How about if x = 2? That would cancel out one of the terms, and simplify things quite a bit.
Now, what if we let x = -3? That would also cancel out one of the terms, right?
And finally, what if we let x = 0? That would cancel out the Ax.
As you can see, we get the exact same result!! Isn’t that so exciting? We completely avoided the grueling part of partial fractions! There is so much less room to make errors, and it is much faster! Please try it out! I’ll post one more example below.
See! Isn’t that much, much easier? Well, I hope you can try it out. I know that partial fractions do not come up all that often, but when they do, you will be very glad you learned this method!
If you liked this post, I bet you would really love my U-Substitution shortcut.
Please comment below or send me an email if you have any questions at all!