00:01
In this question, i'm considering the rational expression 3x squared plus 1 over the quantity of x minus 3 times the quantity of x plus 6 being squared.
00:09
I want to select the one correct partial fraction decomposition expansion.
00:14
We're not going to worry about solving for the coefficient.
00:18
So what i have here are three linear factors in the denominator.
00:23
X minus 3 and then x plus 6 twice.
00:27
I have a repeated linear factor, which means i'm actually going to need three fractions on that right hand side.
00:38
So for my first denominator, i'm going to take x minus 3.
00:44
Now the x plus 6 is being squared.
00:47
Since it is a repeated factor, what i have to do is use that to every power less than or equal to the power that i see, which in this case is 2.
00:57
So i'm going to have my second denominator being x plus 6, while my third denominator is going to be x plus 6 quantity squared...