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Mathematics 19 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

are you looking for an answer or the process?

OpenStudy (anonymous):

both

OpenStudy (anonymous):

well first your need to set up the equivalence \[\frac{9x^2-3x-9}{x^3(x+3)}=\]\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x+3}\]

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

Thats whats confusing me

OpenStudy (anonymous):

what is confusing me is that this interface is buggy

OpenStudy (anonymous):

now it works...

OpenStudy (anonymous):

yea

OpenStudy (anonymous):

then rewrite that as \[9x^2-3x-0=\]\[Ax^2(x+3)+Bx(x+3)\]\[+C(x+3)+Dx^3\]

OpenStudy (anonymous):

that should be a 9 where that 0 is

OpenStudy (anonymous):

k

OpenStudy (anonymous):

then rewrite that as \[9x^2-3x-9=\]\[Ax^2(x+3)+Bx(x+3)\]\[+C(x+3)+Dx^3\]

OpenStudy (anonymous):

so are we good to this point?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

now we can choose x=0 and determine that C=-3

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

and next let x=-3 to determine that D=-3

OpenStudy (anonymous):

are you good with what I am doing?

OpenStudy (anonymous):

yea i get it

OpenStudy (anonymous):

now 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

OpenStudy (anonymous):

alright

OpenStudy (anonymous):

so I chose x=1 and got 3=A+B

OpenStudy (anonymous):

Ok

OpenStudy (anonymous):

next I chose x=-1 and got 3=A-B

OpenStudy (anonymous):

adding those equations together I get 6=2A which says A=3

OpenStudy (anonymous):

then using A=3 in either of the other two either of the previous two equations I determine that B=0

OpenStudy (anonymous):

Now finally substituting those values for A,B,C,D we get\[\frac{9x^2-3x-3}{x^3(x+3)}=\]\[\frac{3}{x}-\frac{3}{x^3}-\frac{3}{x+3}\]

OpenStudy (anonymous):

ok i see

OpenStudy (anonymous):

Thats alot!

OpenStudy (anonymous):

your welcome, glad you followed it. Long process...

OpenStudy (anonymous):

oh yea

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