00:01
So for problem 13, we're asked the exact same thing to simplify the given expression, x squared plus 12x, plus 36, all over x squared minus 36.
00:15
So to simplify the expression and to also identify the values that need to be excluded from the domain.
00:23
So first we need to factor our numerator and denominator.
00:30
Our numerator, we can use that trick that i've been using since number one, where we put our c in the top and our b in the bottom.
00:38
Two numbers that multiply together to give us 36 while adding together to give us 12, and that is going to be 6 and 6.
00:46
6 plus 6 is 12, 6 times 6 is 36.
00:49
So when we split those two up, we can see that we have x plus 6 times x plus 6.
00:57
Now to factor our denominator.
01:01
So our denominator you can see is a difference of two squares.
01:04
We've got x squared minus 36, which is a perfect square.
01:08
So if you know this rule, you should be able to see that this is going to be x plus 6 times x minus 6.
01:15
But if you don't, you can expand this out to x squared plus 0x minus 36.
01:22
So these two are equal.
01:24
And then you can use that trick where we have negative 36.
01:28
And zero.
01:30
So two numbers that multiply together to give us negative 36 while adding together give us 0...