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anonymous
 5 years ago
Find the partial fraction decomposition of the rational function.
9x^2 − 3x − 9
x^4 + 3x3
anonymous
 5 years ago
Find the partial fraction decomposition of the rational function. 9x^2 − 3x − 9 x^4 + 3x3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you looking for an answer or the process?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well first your need to set up the equivalence \[\frac{9x^23x9}{x^3(x+3)}=\]\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x+3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thats whats confusing me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is confusing me is that this interface is buggy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then rewrite that as \[9x^23x0=\]\[Ax^2(x+3)+Bx(x+3)\]\[+C(x+3)+Dx^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that should be a 9 where that 0 is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then rewrite that as \[9x^23x9=\]\[Ax^2(x+3)+Bx(x+3)\]\[+C(x+3)+Dx^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so are we good to this point?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now we can choose x=0 and determine that C=3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and next let x=3 to determine that D=3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you good with what I am doing?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now however we are going to need to choose two different values of x and get a system of two equations in two variable tosolve for A and B

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so I chose x=1 and got 3=A+B

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0next I chose x=1 and got 3=AB

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0adding those equations together I get 6=2A which says A=3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then using A=3 in either of the other two either of the previous two equations I determine that B=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now finally substituting those values for A,B,C,D we get\[\frac{9x^23x3}{x^3(x+3)}=\]\[\frac{3}{x}\frac{3}{x^3}\frac{3}{x+3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0your welcome, glad you followed it. Long process...
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