Question

partial fraction decomposition (a s^2+b s+c)/(s^3 (s+d)) where a,b,c,d are known constants

Answer 1

hi,
do you know normal partial process, with say
(Ax+B)(Cx+D) type of denominators ?

Answer 2

yes , I just havent' done partials in a very long time and could use some help

Answer 3

i can solve it, just determining numerators and denominators is tripping me up, can you help?

Answer 4

sure

Answer 5

\(\Large \dfrac{as^2+bs+c}{s^3(s+d)}=\dfrac{A}{s+d}+\dfrac{B}{s}+\dfrac{C}{s^2}+\dfrac{D}{s^3}\)
do you understand this form ?

Answer 6

and have any idea how to get A,B,C,D ??

Answer 7

still there ?
bdw, even i love to laugh :D

Answer 8

no they're just known constants

Answer 9

ok

Answer 10

do you know how to take the LCM while adding fractions ?

Answer 11

like for example x/y +z/y^2 will be (xy+z)/y^2

Answer 12

from this ,
\(\Large \dfrac{as^2+bs+c}{s^3(s+d)}=\dfrac{A}{s+d}+\dfrac{B}{s}+\dfrac{C}{s^2}+\dfrac{D}{s^3}\)

could you understand how i get
\(as^2+bs+c=A(s^3)+Bs^2(s+d)+Cs(s+d)+D(s+d)\)

Answer 13

from this, its not that difficult,
to get A put s=-d