00:01
We're being asked to add the given rational expressions.
00:03
Well, similar to adding fractions, we're going to need a common denominator.
00:07
So we're going to start by factoring each denominator.
00:10
So first, we have x squared plus 6x plus 9.
00:13
Well, if it's going to factor, it will factor the two binomials.
00:16
The next thing is the coefficient of x squared is 1, so we know they both start with x.
00:21
So what multiplies to 9 that adds to 6? will that be positive 3 and positive 3? so now we have our two factors.
00:28
For our second denominator, x squared minus 9, that's the difference of two squares.
00:32
So we'll have x plus 3 and then x minus 3.
00:36
And for our last denominator, we can't actually factor x minus 3, so we leave that as it.
00:41
So now we need all these factors to be the same, or our denominators to be the same.
00:46
Well, i notice the first one is missing that x minus 3 factor.
00:49
So we'll put that in.
00:51
Compared to the first denominator, the second one is missing another x plus 3, and the last denominator is missing both x plus 3s.
01:02
So now we have our common denominator.
01:04
And whatever we multiply the denominator by, we have to go and multiply the numerator by it as well.
01:14
All right.
01:15
So first, we're going to have to distribute x minus 3 to both terms 4x plus 12.
01:20
Well, x times 4x is 4x squared.
01:23
X times 12 is positive 12x.
01:26
Negative 3 times 4x is negative 12x, and negative 3 times 12 is 9 .000 is 9.
01:32
Negative 36.
01:34
And our denominator is x minus 3 times, and notice both x plus 3s are the same factor, so we can write that as x plus 3 squared.
01:45
For our second one, we have to distribute the 5x, which will give us 5x squared plus 15x all over x plus or x minus 3 times x plus 3 squared.
01:58
Now for our last one, remember, x plus 3 times x plus 3 was this denominator x squared plus 6x plus 9.
02:06
So now we just have to distribute the 7, which will give us 7x squared plus 42x plus 63.
02:14
And again, over our common denominator x minus 3 times x plus 3 squared.
02:21
Well, now that we're adding these fractions, we just have to go ahead and combine like terms.
02:25
So let's start with our x squared terms.
02:27
We have 4x squared plus 5x squared.
02:30
That would be 9x squared...