Question

partial fractions problem...

Answer 1

\[\frac{ 2s-4 }{ (s ^{2}+5)(s^{2}+1) }\]

Answer 2

@zepdrix @dan815 @amistre64

Answer 3

just let me know how to break it down...

Answer 4

\[\frac{2s-4}{(s^2+5)(s^2+1)}=\frac{As+B}{s^2+5}+\frac{Cs+D}{s^2+1}\]

Answer 5

i thought so

Answer 6

im want to find the laplace of it at the end.

Answer 7

i*

Answer 8

i solved it but im getting the wrong answer apparently.

Answer 9

The inverse transform, you mean?

Answer 10

what do u get for ur variables?

Answer 11

yeah dont worry about that, just please let me know what are your variables.

Answer 12

i get A=-.5, B=1, C=.5, D=-1.

Answer 13

\[\frac{2s-4}{(s^2+5)(s^2+1)}=\frac{As+B}{s^2+5}+\frac{Cs+D}{s^2+1}\\
2s-4=(As+B)(s^2+1)+(Cs+D)(s^2+5)\\
2s-4=As^3+Bs^2+As+B+Cs^3+Ds^2+5Cs+5D\\
2s-4=(A+C)s^3+(B+D)s^2+(A+5C)s+(B+5D)\]
Yielding the system
\[\begin{cases}A+C=0\\B+D=0\\A+5C=2\\B+5D=-4\end{cases}~\Rightarrow~\begin{cases} A=-\frac{1}{2}\\\\B=1\\\\C=\frac{1}{2}\\\\D=-1\end{cases}\]

Answer 14

probably the book is wrong!

Answer 15

thanks!

Answer 16

you're welcome

Answer 17

@SithsAndGiggles sorry @zepdrix beat u to it.