Factoring Fractions: Solve (x+20)(x+10)^2+400

[seang]

how do I make:

20(x + 20) / ((x+10)^2 + 400)

into a fraction like (x-a)(x-b)...etc / (x-c)(x-d)...etc

where a b c d are constants. The 400 is really stumping me.

 

[AKG]

It's impossible if a, b, c, d, ... have to be real numbers. If they can be complex, then you can do it. Well, actually, no you technically can't do it because of the 20, but you can come closer to your goal.

 

[Corneo]

I assume you are asking this to find the inverse Laplace transform for your circuit problems. What you don't see is that the form is already in the form that is useful to be inverted.

$$Y(s) = 20 \frac {s+20}{(s+10)^2 + 400} = 20 \frac {s + 10 + 10}{(s+10)^2 + 400} = 20 \bigg[ \frac {s+10}{(s+10)^2+400} + \frac {10}{(s+10)^2 + 400}\bigg]$$

Now look up the Laplace transforms of cosines and sines.