# X(s)=((5s^2−15s+7))/((s−2)^3(s−1)). Which is the impulse response?and which is the exit signal of the system?

There is a timely unchanged continuous function :
$H\left(s\right)=\frac{s-1}{s+1}$
At the entry of the system exists a x(t) which Laplace's transformation is:
$X\left(s\right)=\frac{\left(5{s}^{2}-15s+7\right)}{\left(s-2{\right)}^{3}\left(s-1\right)}$
Which is the impulse response?and which is the exit signal of the system?
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gortepap6yb
Here is how you advance. Use partial fraction to get
$H\left(s\right)=1-\frac{2}{1+s}$
Taking the inverse Laplace gives
$h\left(t\right)=\delta \left(t\right)-2{e}^{-t},$
where $\delta \left(t\right)$ is the Dirac function. Note that, the Laplace transform of the functions $\delta \left(t\right)$ and ${e}^{-t}$ are 1 and $\frac{1}{s+1}$. For the second one use partial fraction
$X\left(s\right)=\frac{17}{{\left(s-2\right)}^{2}}-\frac{17}{\left(s-2\right)}+\frac{17}{\left(s-1\right)}-\frac{27}{{\left(s-2\right)}^{3}}.$
Now, try to finish the problem.