Question

how do I do partial fractions for:

(2+s^2)/((s^2)(s+1)(s+2)) ?

Thanks for the help!

Answer 1

As+b c d
----- + --------- + --------
s^2 s+1 s+2

Answer 2

how do I go from there though?

Answer 3

set it equal to (2+s^2)/((s^2)(s+1)(s+2))

Answer 4

then multiply by denominator

Answer 5

(As+b)(s+1)(s+2)+ c (s^2)(s+2) + d s^2 (s+1) =(2+s^2)

Answer 6

thanks! I think I got it.

Answer 7

Are you working with Laplace transforms?

Break the quotient as follows:
\[\frac{2+s^2}{s^2(s+1)(s+2)}=\frac{As+D}{s^2}+\frac{B}{s+1}+\frac{C}{s+2}.\]Now it's just a matter of solving for A, B and C.
\[(As+D)(s+1)(s+2)+Bs^2(s+2)+Cs^2(s+1)=2+s^2.\]Setting s = -1,
\[B=3.\]Setting s = -2,\[-4C=6\implies C=-\frac{3}{2}.\]Setting s = 0,\[2D=2\implies D=1.\]Finally, \[A=-\frac{3}{2}.\]Therefore,\[\frac{1}{s^2}+\frac{3}{s+1}-\frac{3}{2(s+2)}-\frac{3}{2s}.\]

Answer 8

Too slow. xd

Answer 9

yes, I am :) fun stuff lol.