00:01
We are given two rational equations, 1 divided by 12 a squared minus 4a, and 15 divided by 6a to the 4th minus 3a cubed.
00:09
So when we're trying to find the least common denominator, what we have to do is look at these two denominators and factor them.
00:16
So 12a squared minus 4a, or we can factor out the 4a.
00:21
We get 3a minus 1.
00:24
This becomes 4a times 3a times 3a minus 1.
00:30
We can't factor out the 3 8 anymore, 3a minus 1 anymore, so we leave it as its own factor.
00:36
And now we have 4 times a here, which is also 2 times 2 times a.
00:42
So the unique factors here are 2a and 3a minus 1.
00:48
And as you can see, a occurs once, 38 minus 1 occurs once and 2 occurs twice.
00:54
Over here and over here.
00:56
So now we can move on to the next denominator, which is 6a to the fourth minus 2a cubed, which is equal to 2a cubed times 3a minus 1.
01:11
And again, we can't factor out the 3a1 minus 1 anymore, so leave it here...