# Math Help - Inverse Laplace Transform

1. ## Inverse Laplace Transform

Find the IVL of $\frac{(s-2)e^{-s}}{s^2-4s+3}$.

I am not understanding how my textbook gets the answer $u_1(t)e^{2(t-1)}cosh(t-1)$

I end up with

$e^{-s}\left(\frac{1}{2(s-1)}+\frac{1}{2(s-3)}\right)$

$=u_1(t)\left(\frac{1}{2}e^{(t-1)}+\frac{1}{2}e^{3(t-1)}\right)$

2. Originally Posted by petition Edgecombe
Find the IVL of $\frac{(s-2)e^{-s}}{s^2-4s+3}$.

I am not understanding how my textbook gets the answer $u_1(t)e^{2(t-1)}cosh(t-1)$

I end up with

$e^{-s}\left(\frac{1}{2(s-1)}+\frac{1}{2(s-3)}\right)$

$=u_1(t)\left(\frac{1}{2}e^{(t-1)}+\frac{1}{2}e^{3(t-1)}\right)$
$= u_1(t) e^{2(t-1)} \left(\frac{1}{2}e^{-(t-1)}+\frac{1}{2}e^{(t-1)}\right) \, ....$

3. OK, so my answer wasn't wrong, it just wasn't simplified. I've got to remember my hyperbolic functions.