00:01
This problem wants us to perform the indicated operation of addition between 6 divided by x minus 3 plus 8 over 3 minus x.
00:08
And when we're adding and subtracting rational expressions, we do need a common denominator.
00:12
And it can be easy to look at these and quickly think that they're the same just because you see an x and a 3.
00:18
But one is x minus 3, and one is 3 minus x.
00:21
And the difference is a little easier to see when we put our denominators in standard form, which means the highest exponent of our variables comes first and then working all the way down to our constants.
00:32
And 6 over x minus 3 has x minus 3 already in standard form.
00:36
But for 8 over 3 minus x, we would switch these two terms around, and the x would keep its negative.
00:42
So that's negative x, and the 3 is positive.
00:45
So that's a plus 3.
00:46
Now it's a little easier to see that these aren't quite matching up.
00:49
But before we just automatically multiply each fraction by the other's denominator, we can factor this negative out from the negative x plus 3...