Hey, I cannot figure out how to get these two probelms figured out. I need to find the inverse of the laplace transform.

Here is what ive tried: given H(s) find h(t). (take inverse laplace transform)

1) $\displaystyle H(s)=\dfrac{s^{2}-3s+9}{(s^{2}+16)^{2}}$

using partial fractions I split this up into:

$\displaystyle \dfrac{1}{s^{2}+16}+\dfrac{-3s-7}{(s^{2}+16)^{2}}$

I know:

$\displaystyle \dfrac{1}{s^{2}+16}=\dfrac{1}{4}sin(4t)$

which leaves me with:

$\displaystyle \dfrac{-3s-7}{(s^{2}+16)^{2}}$

From here i cant seem to split this up any further into a sin/cos/e^(x) or other simple function. Any help on the next step, or corrections to what I have already done would be great.

2) given K(s) find k(t) (take inverse of laplace transform).

$\displaystyle K(s)=\dfrac{2s}{s^2-6s+25}$

I cant factor the denominator so i tried writing the demoninator in various ways which didnt lead me anywhere. Without being able to split the denominator up I also cannot use partial fractions to help simplify this. Any ideas?

$\displaystyle K(s)=\dfrac{2s}{(s^2+16)+(-6s+9)}$, didn't seem to help.