How do I break this up into partial functions?
(s^4+81)/ s(s^2+9)^2
Not sure what i should be splitting it up to

Question

How do I break this up into partial functions?
(s^4+81)/ s(s^2+9)^2
Not sure what i should be splitting it up to

anonymous · Answer

I get someone like A/s + B/(s^2+9) + c/(s^2+9)^2

amistre64 · Answer

a/s
b/(s^2+9)
c/(s^2+9)^2

where a b and c are the appropriate poly substitutions

amistre64 · Answer

s^2 requres the ax+b linear top for completeness

amistre64 · Answer

same with the other quad, needs a linear atop it

anonymous · Answer

Ugh So I was kinda right? Not sure how to finish that. Do I solve for ABC, then split up the equation with B in it?

anonymous · Answer

ick

anonymous · Answer

$$\frac{a}{s}+\frac{bx+c}{(x^2+9)}+\frac{dx+e}{(x^2+9)^2}$$ lordamercy
fortunately b = c = 0

anonymous · Answer

$$a(x^2+9)^2+(bx+c)x(x^2+9)+(dx+c)x=x^4+81$$

anonymous · Answer

replace x  by 0, get 
$$81a=81$$
$$a=1$$ so that part was easy

anonymous · Answer

So I got a=1

anonymous · Answer

yep

anonymous · Answer

now i think you have to expand  and equate like coefficients

anonymous · Answer

So i just need to find  d and e right?or is there more to it?

anonymous · Answer

assuming we grant that b and c are both zero, yes
but i am not sure we get to assume that

anonymous · Answer

anonymous · Answer

that seems obsurd..

amistre64 · Answer

hmm, did you do a fancy substitution with s=x for the others ?  :)