Rationalizing: (5s^2-20s+36)/((s-2)(s^2-4s+20))

[gtfitzpatrick]

(5s$$^{2}$$-20s+36)/((s-2)(s$$^{2}$$-4s+20)

expanding out i just inputed

EXPAND((5·s^2 - 20·s + 36)/((s - 2)·(s^2 - 4·s + 20)), Rational, s)

but trying to L$$^{-1}$$ does anyone have any ideas?

i tried

LAPLACE((5·s^2 - 20·s + 36)/((s - 2)·(s^2 - 4·s + 20), t, S)·s  Real (0, ∞)

should i just do it by its parts or can i do it whole?

 

[Defennder]

First decompose that expression into partial fractions. Then apply the inverse Laplace transform to the individual fraction expressions. In general that's how you find the inverse Laplace transform for complicated expressions.