Heya, I have a few questions about partial fraction decomposition.
1) If the given denominator has only a repeated factor, i.e., p(s)/(q(s)^n) as opposed to p(s)/(r(s)q(s)^n), does that entail that the fraction cannot be further decomposed?
2) Is there a way to decompose fractions if the given denominator has factors raised to non-integer powers, i.e., s/((s - 3)(s + 1)^2.5)?
3) Is it normal to get incorrect answers if you don't fully factor the given denominator before decomposing? I don't have the exact fraction I was working, but it was something like p(s)/((s + 1)(s^2 - 4), and I wanted to decompose it into A/(s + 1) + (Bs + C)/(s^2 - 4) (to do cosh(2t) and sinh(2t) Inverse Laplace Transforms for the latter term). I kept getting the wrong answer until I broke up the s^2 - 4. Is this outcome expected when the denominator is only partially factored, or was is likely a calculation error?
1) If the given denominator has only a repeated factor, i.e., p(s)/(q(s)^n) as opposed to p(s)/(r(s)q(s)^n), does that entail that the fraction cannot be further decomposed?
2) Is there a way to decompose fractions if the given denominator has factors raised to non-integer powers, i.e., s/((s - 3)(s + 1)^2.5)?
3) Is it normal to get incorrect answers if you don't fully factor the given denominator before decomposing? I don't have the exact fraction I was working, but it was something like p(s)/((s + 1)(s^2 - 4), and I wanted to decompose it into A/(s + 1) + (Bs + C)/(s^2 - 4) (to do cosh(2t) and sinh(2t) Inverse Laplace Transforms for the latter term). I kept getting the wrong answer until I broke up the s^2 - 4. Is this outcome expected when the denominator is only partially factored, or was is likely a calculation error?
