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Nanoman
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.
What I get is\[x-36+\frac{972x+11664}{x^2+36x+324}\]
ohhh....right. I had that down on paper but typed it wrong on here.
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
\[x-36+\frac{972x+11664}{x^2+36x+324} \\ \\\frac{972x+11664}{(x+18)^2}=\frac{A}{(x+18)}+\frac{B}{(x+18)^2}\]
\[972x+11664=A(x+18)+B \\ \\ \] When x=-18 B=-5832 When x=0 18A-5832=11664 A=972 \[x-36+\frac{972x+11664}{x^2+36x+324} \\ \\\frac{972x+11664}{(x+18)^2}=\frac{972}{(x+18)}-\frac{5832}{(x+18)^2}\]
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.