00:01
Okay, in this problem we have to divide these two rational expressions.
00:05
So the first thing i need to do is i need to multiply by the reciprocal of my denominator.
00:10
So i'm going to rewrite this as a multiplication problem, and i also, after that, i need to factor.
00:16
So let's get to work.
00:17
3y minus 7y minus 6.
00:19
So we have 3y minus, or 3y squared, minus 7y minus 6 over, what is our second term? 2y squared minus 3y minus 9.
00:29
2y squared minus 3y minus 9.
00:33
And then we're going to multiply by flipping this fraction right here.
00:36
We have 2y squared plus y minus 3 over y squared plus y minus 2.
00:44
So now we get to work factoring both of these.
00:46
So we say, what are the factors of 6 that when i multiply those together and multiply one of those by 3, do i get negative 7? so i'm going to write that as 3y, and then the next one is just going to be y.
01:00
And then i need to ask myself, well, okay, i need to get negative 7, so i'm going to make this negative 2, right? so you give me negative 6.
01:08
No, it's not going to be actually going to, excuse me, it's going to be minus 3, so that i'll have 3 times negative 3y times negative 3, and that'll give me negative 9.
01:16
And then i'm going to write plus 2 here.
01:19
So notice we have 2 times negative 3 will give us our negative 6.
01:22
And then we'll have negative 9y plus 2y for our negative 7y on the bottom.
01:27
Okay, now we can move on to the bottom, right? so we'll have 2y, come on computer, 2y here, and then we'll have y here.
01:36
Now we need the factors of negative 9 that when i combine them, i'm going to get negative 3, where one of them is multiplied by 2.
01:43
So what are the factors of 9? maybe 3 and 3? so that'll be, yeah, that'll do.
01:48
We need negative, so this will be 3 right here, and this will be positive 3 right here, and that'll give us our negative 6y plus 3y, which will give us our negative 3y right there, and we're done with that one...