- #1
themadhatter1
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Homework Statement
Write the Partial Fraction decomposition for:
[tex]\frac{x}{16x^4-1}[/tex]
Homework Equations
The Attempt at a Solution
[tex]\frac{x}{16x^4-1}[/tex]
[tex]=\frac{x}{(2x-1)(2x+1)(4x^2+1)}[/tex]
[tex]=\frac{x}{(2x-1)(2x+1)(4x^2+1)}=\frac{a}{(2x-1)}+\frac{b}{(2x+1)}+\frac{cx+d}{4x^2+1}[/tex]
[tex]x=(2x+1)(4x^2+1)a+(2x-1)(4x^2+1)b+(2x-1)(2x+1)(cx+d)[/tex]
From here I can find that A=1/8 and B=1/8
I can't find c and d because I would have to plug in i/2 into x to get [tex](4x^2+1)=0[/tex]
Now, I believe I need to set up a system of equations. I can foil and get what I had into polynomial form and I'd get.
[tex]x=(8a+8b+4c)x^3+(4a-4b+4d)x^2+(2a+2b-c)x+(a-b-d)[/tex]
From here I'm not quite sure what to do to create the system of equations.
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