# [SOLVED] Partial Fractions #1

• Jul 6th 2008, 12:00 PM
redman223
[SOLVED] Partial Fractions #1
I just have to write out the form of the partial fraction decomposition.

$\displaystyle \frac {x^4} {(x^3+x)(x^2-x+3)}$

Now when the fraction is improper you are supposed to use long division right? But how does that work with more than one term in the denominator? I came up with $\displaystyle \frac {A}{x} + \frac {Bx+C}{(x^2+1)} + \frac {Dx+E}{(x^2-x+3)}$ but I don't think that is right as I did not use long division.

The reason I didn't use long division was because if you multiply out the denominator, the fraction turns into a proper fraction, with the numerator having the lower power. But when you factor out the bottom, it switches. I don't know what to do in this situation.
• Jul 6th 2008, 12:19 PM
o_O
That is correct. Long division isn't needed because the degree of the numerator is already less than that of the denominator (if you multiplied the denominator out, you'll see the highest power is $\displaystyle x^5$).