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# partial fractions watch

1. for 1/(1+x^3),

I've got to = A/(x+1) + B/(x^2 -x+1)

But the values of A and B are different depending on x. So they must include an x term? Where do I go from here?
2. (Original post by pippabethan)
for 1/(1+x^3),

I've got to = A/(x+1) + B/(x^2 -x+1)

But the values of A and B are different depending on x. So they must include an x term? Where do I go from here?
You need to have a polynomial term on top of the fraction which is 1 order lower than the denominator
EDIT: this is good for most, repeated denominator terms are different though
3. (Original post by pippabethan)
for 1/(1+x^3),

I've got to = A/(x+1) + B/(x^2 -x+1)

But the values of A and B are different depending on x. So they must include an x term? Where do I go from here?
It should be

If your partal fraction term has polynomial of degree n in the denominator, then the numerator should be of degree n-1. Which is why linear term at the bottom => constant term on top. Quadratic in bottom (like x^2 - x +1) => linear term on top.
4. Aha thank you both! I'll give it another go
5. is this still the case if the denominator is (ax+b)^2 ?
6. (Original post by pippabethan)
is this still the case if the denominator is (ax+b)^2 ?
No, if the denominator is then you do .

7. (Original post by Zacken)
No, if the denominator is then you do .

Thank you
8. (Original post by pippabethan)
is this still the case if the denominator is (ax+b)^2 ?
It becomes more complicated. If I had 1/(ax+b)(cx+d)^2 this would be split into A/(ax+b) + B/(cx+d) + (Cx+D)/(cx+d)^2
9. (Original post by EwanWest)
It becomes more complicated. If I had 1/(ax+b)(cx+d)^2 this would be split into A/(ax+b) + B/(cx+d) + (Cx+D)/(cx+d)^2
But @Zacken just said this would be C/(cx+d)^2 ??
10. (Original post by pippabethan)
But @Zacken just said this would be C/(cx+d)^2 ??
Yes he's correct, I haven't done these in a while. Having said that if you have the extra term in there like I do it will just come out as 0 when you compare coefficients so it won't give you the wrong answer
11. (Original post by pippabethan)
But @Zacken just said this would be C/(cx+d)^2 ??
That's correct.

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Updated: September 11, 2016
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