Question

Hi I am having trouble with this type of partial fraction decompisition. 2/(x^3 + x^2)

Answer 1

I think I need A B and C...the needing 3 parts is what is confusing me.

Answer 2

\[\Large \frac{2}{x^3+x^2}\quad=\quad \frac{2}{x^2(x+1)}\]Hmm so I guess that's as far as we want to factor it.
having a bit of trouble getting the proper setup?

Answer 3

We have a repeated linear factor `x` in the bottom, so we have to do something fancy for that one.\[\Large \cfrac{2}{x^2(x+1)} \quad=\quad \cfrac{A}{x}+\cfrac{B}{x^2}+\cfrac{C}{x+1}\]Mmmmm yah, I think this is the setup that we want.

Answer 4

@zepdrix's setup works nicely!

Answer 5

Partial fractions have never made a ton of sense to me so I can't think of the proper way to explain this...

Notice the bottom you can write as x*x*(x+1)
So we have a repeated linear factor of x.

There is a special way we deal with those types of things.
I would recommend googling `partial fraction decomposition repeated factors` if you want to get some better understanding of that rule.

Hmm, so do you understand how to solve the problem from that setup?

Answer 6

so A/x + B/x^2 +C/x+1) ?

Answer 7

ok thank you!