00:01
All right, so our function right now is 8 s squared minus 4 s plus 12 over s times s squared plus 4.
00:09
And so if you look at a denominator, it's already factored.
00:11
So it might be a good idea to start with trying partial fraction decomposition.
00:16
So of a over s plus, and we have a function like s squared plus another thing squared, so this is 4, so it be 2 squared.
00:25
You're going to use bs plus c as your numerator over s squared.
00:30
Plus 4.
00:32
So now multiply it all out.
00:34
We're going to have as squared plus 4, a plus b s squared plus plus c s equals our numerator, which i'll rewrite this lower, so this is going to be any.
00:52
We'll rewrite this round of our room.
00:59
Okay, well, okay.
01:04
So this is going to be a s squared plus 4a plus b s squared plus c s equals 8 s squared minus 4 s plus 12 um and then so we can separate it all out we have a s squared plus b s squared is equal to 8 s squared so that's one equation and then we'll have uh so now we'll look at our s terms so we only have c times s, so if c s is equal to our s terms in the on our right side, which is negative 4s.
01:50
And now we'll look for our terms of no s, which is 4, a, and 12.
01:56
So these will be pretty easy to solve.
01:58
Divide both by 4, we'll have a equals 3.
02:03
Divide both by s.
02:04
Let's see equals negative 4.
02:08
Let me erase that line there.
02:12
So it was in here 4, divide all these...