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Resolve into partial fraction\[\frac{x^2}{x^41}\]\[\frac{x^2}{x^41}=\frac{x^2}{(x^2+1)(x1)(x+1)}\]
\[A(x1)(x+1) + B(x^2+1)(x1) + C(x^2+1)(x+1) = x^2\]\[(B+C) x^3+(AB+C)x^2 +(B+C)x AB+C =x^2\]So, B+C = 0, AB+C=1, A+BC = 0
And I got A = 1/2, B=1/4, C=1/4
So,
\[\frac{x^2}{x^41} = \frac{1}{2(x^2+1)}  \frac{1}{4(x+1)} +\frac{1}{4(x1)}\]
 one year ago
 one year ago
Is that correct? Resolve into partial fraction\[\frac{x^2}{x^41}\]\[\frac{x^2}{x^41}=\frac{x^2}{(x^2+1)(x1)(x+1)}\] \[A(x1)(x+1) + B(x^2+1)(x1) + C(x^2+1)(x+1) = x^2\]\[(B+C) x^3+(AB+C)x^2 +(B+C)x AB+C =x^2\]So, B+C = 0, AB+C=1, A+BC = 0 And I got A = 1/2, B=1/4, C=1/4 So, \[\frac{x^2}{x^41} = \frac{1}{2(x^2+1)}  \frac{1}{4(x+1)} +\frac{1}{4(x1)}\]
 one year ago
 one year ago

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RolyPolyBest ResponseYou've already chosen the best response.0
@zepdrix Yes! That should be the case, but I can't get the answer by solving that equation :(
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.0
Continue from that step; (A+C+D)x^3 + (B+CD)x^2 + (A+C+D) + (B+CD) = x^2 So, A+C+D = 0  (1) (B+CD) = 1  (2) A+C+D =0  (3) B+CD = 0  (4) (1)(3): A=0 (3)(4): A+B = 0 => B = 0 Here comes the problem!
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1350711031547:dw Hmmmm we have 4 equations and 4 unknowns. This should be solvable. It might be a bit of work though :o
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1350711417164:dw Hmm maybe just try combining them a different way? <:O I came up with this, let me know if my math was incorrect.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
I'm also getting A=0, I don't think that's a problem though. Since I was able to get a B term.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Oh i see the problem, (3)(4) = (A+C+D)  (B+CD) = A + B +2D = 0
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.0
Uhhuh! My mistake!! Thanks :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yah these things suck :) lol
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.0
(2)  (4): B = 1/2 Yay!
 one year ago
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