00:02
Okay, this question wants us to decompose this expression using partial fractions.
00:07
So, to do that, we have to figure out what the denominator factors into.
00:16
Well, first, we can pull out a factor of x from each term, but, as you can see, we're not done yet, because we have a difference of squares down there, so we can factor it again.
00:39
And now we can write our decomposition.
00:43
So these are all just linear factors.
00:45
So we just get an a over x plus a b over x plus 2, plus a c over x minus 2.
00:55
So now let's write a system to solve for a, b, and c.
01:00
So again, just rewriting what we had over there, we get our partial fraction decomposition.
01:28
All right, so let's multiply by that denominator on the right to clear our fractions.
01:37
So our a term gets the fraction parts it didn't get originally.
01:44
There should be a two.
01:47
Then our b term gets the parts it didn't have originally.
01:53
And then the c term gets the parts it didn't have originally.
02:10
So now, with this method, foiling this all out could be quite complicated...