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Nanoman

  • 2 years ago

Partial fractions question: x^3 -------------------- x^2 + 36x + 324 I used polynomial long division on this, and got: x+ 36 + 972x + 1166 -------------- x^2 + 36x + 324 I've gotten to the point where the partial fraction is 972x + 1166 = Ax 18A + B. A = 972, but I can't find out what B is.

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  1. .Sam.
    • 2 years ago
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    What I get is\[x-36+\frac{972x+11664}{x^2+36x+324}\]

  2. Nanoman
    • 2 years ago
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    ohhh....right. I had that down on paper but typed it wrong on here.

  3. .Sam.
    • 2 years ago
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    |dw:1362057398152:dw|

  4. hartnn
    • 2 years ago
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    to find out B, you can put x=0 in 972x + 1166 = Ax 18A + B. and you already know A , so you'll get B

  5. .Sam.
    • 2 years ago
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    \[x-36+\frac{972x+11664}{x^2+36x+324} \\ \\\frac{972x+11664}{(x+18)^2}=\frac{A}{(x+18)}+\frac{B}{(x+18)^2}\]

  6. .Sam.
    • 2 years ago
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    \[972x+11664=A(x+18)+B \\ \\ \] When x=-18 B=-5832 When x=0 18A-5832=11664 A=972 \[x-36+\frac{972x+11664}{x^2+36x+324} \\ \\\frac{972x+11664}{(x+18)^2}=\frac{972}{(x+18)}-\frac{5832}{(x+18)^2}\]

  7. Nanoman
    • 2 years ago
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    Thanks Sam, I really appreciate it. I was trying to move the terms around to get the answer, but just plugging it in works well.

  8. .Sam.
    • 2 years ago
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    welcome :)

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