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anonymous
 5 years ago
Find the partial fraction decomposition of the rational function.
5x^2 + 8/x3 + x2
anonymous
 5 years ago
Find the partial fraction decomposition of the rational function. 5x^2 + 8/x3 + x2

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is this \(\frac{5x^2+8}{x^3+x^2}\)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0got a 5x^2 + 8 = A/x^2 + B/x + 1 A(x+1) + B(x^2) (Ax+A) + (Bx^2) (Ax + Bx^2) + A 5x^2 + 8 = (A + B) x + (A)x^2 5x^2+x+8=(A+B) + (A)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the x^2 is throwing me off

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So the problem is in how you split it up in the first step. First you've got to realize that the denominator splits into a factor that gets taken into a power. Namely, \(x^3+x^2\) becomes \(x^2(x+1)\), where \(x\) is a factor taken to the second power. The split up thus goes as follows: \[ \begin{align*} \frac{5x^2+8}{x^3+x^2} &= \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}\\ 5x^2+8 &= Ax(x+1) + B(x+1) + Cx^2 \end{align*} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0where did the A/x come from?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So the \(\frac{A}{x}\) comes from the fact that the \(x\) factor is taken to a power. As another example, if we had taken \(\frac{1}{(x+1)^2}\), the decomposition would split into \(\frac{A}{x+1} + \frac{B}{(x+1)^2}\).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Can you solve the problem from there, then?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0shouldnt the next step be 5x^2 + 8= (Ax^2+Cx^2) + (Ax+Bx) +B? After combining terms?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok thanks for your help!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is 7/x + 8/x^2 + 12/x+1 the right answer?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I got a different answer from that. You can see that something is off because \(A+B\) should equal \(0\), as there is no \(x\) term on the left hand side.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So how did you go about solving once you combined terms?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.05x^2+8=(A+C)x^2 + (A+B)x + B 5x^2 +0x+8=(A+C) + (A+B) + B then i put it on the matrix function on my calculator and it gave me 7, 8 and 12.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats how i got Is 7/x + 8/x^2 + 12/x+1.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You probable plugged some numbers in wrong. I get 8, 8, and 13.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me see if that works.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thats it. I dont understand what i did arong though?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I had 1 0 1 5 1 1 0 1 0 1 0 8 as my matrix.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Row 2, column 4 should be a 0, not a one, as there's no \(x\) term.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ah i see the 0x term stays zero and not 1.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Alright I have now. Thank you so much for helping me. I really appreciate it!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No problem, glad you understood it!
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