I need to use partial fractions on this term:
this term (note: it said :
and lastly this term
I am stumped because I have tried all the methods that worked on the prior problems (which were easier no doubt) but I keep running into an impasse. Can anyone please help? I'm in differential equations (doing the chapter on LaPlacian's) but this is definitely from calculus. Thank you!
Kind Regards,
Andy
First of all, it's helpful to know the rule that the number of constants will always equal the total degree of the original denominator. In this case, the degree is 3, so there should be exactly 3 constants used.
Since the second term can't be factored and doesn't have degree 1, we need to use multiple constants. (The number of constants is determined by the degree of that term.) So:
That's it. You can now try to solve for the constants.
For this one, we should probably combine it into a single fraction first. (Alternatively, you can use partial fractions separately for each term or whatever, but this simplifies somewhat.)this term (note: it said :
Now, our denominator is comprised of two terms, both with multiplicity of 2, and neither can be reduced any further, so:
You already broke this one apart correctly. Is there a problem solving for the constants?and lastly this term