Question

Partial fractions question:

x^3
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x^2 + 36x + 324

I used polynomial long division on this, and got: x+ 36 + 972x + 1166
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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.

Answer 1

What I get is\[x-36+\frac{972x+11664}{x^2+36x+324}\]

Answer 2

ohhh....right. I had that down on paper but typed it wrong on here.

Answer 3

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

Answer 4

\[x-36+\frac{972x+11664}{x^2+36x+324} \\ \\\frac{972x+11664}{(x+18)^2}=\frac{A}{(x+18)}+\frac{B}{(x+18)^2}\]

Answer 5

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

Answer 6

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.

Answer 7

welcome :)