00:01
All right guys, so we have this addition and subtraction problem with fractions and some variables y and x.
00:08
So our first step in any problem like this is to get common denominators, which we don't have, because here are denominators x minus y and on the other side's y minus x.
00:16
And we're going to give a denominator to two by putting it over one.
00:20
So all three denominators are different.
00:22
So to get a common denominator, we're going to have to figure out what the least common multiple of all of these are.
00:27
And we're going to do that by multiplying each binomial by the other one.
00:32
And what i mean by that is we'll multiply x minus y by y minus x and vice versa on this side.
00:40
We'll multiply by x minus y.
00:42
So now both of these are equal, the left and right ones, the left and right parts of this expression.
00:48
And we'll put the same value over these multiplied denominators so that we're not actually changing our expression.
00:55
And for our middle expression, i'm going to put the multiple.
00:58
A little below it, right down here we're going to multiply by y minus x times x minus y.
01:06
So that's also equal to the other two.
01:09
And we'll put the same thing on top again so we don't actually alter this expression, y minus x times x minus y.
01:18
And then let's just simplify.
01:19
So we're going to find our common denominators and find the numerator.
01:23
So let's start from the left.
01:24
Let's distribute our y value to this binomial.
01:27
So y times y is y squared.
01:30
Y times negative x here is minus xy.
01:35
And we'll put that over our common denominator, y minus x times x minus y.
01:45
Our middle value right now we're going to just write as plus two times y minus x times x minus y over the same denominator as our left part of the expression because we found common denominators times x minus y.
02:09
And finally our right side, we're going to subtract x times x is x squared plus x times negative y is minus xy over the same denominator as the other two.
02:26
So y minus x times x minus y and x minus y.
02:32
All right.
02:33
So now what we have to do is combine this into one fraction and combine like terms in the numerator.
02:40
So right now, i'm going to switch this subtraction to an addition and switch the signs of both parts of this expression.
02:47
So this becomes a negative x squared and a positive xy, just to keep us from reading confused later on.
02:53
So let's write this one big fraction where we have our common denominator, because you never add or subtract denominators.
02:59
We'll just carry it through, y minus x times x minus y.
03:05
And on the top, we combine like terms.
03:08
So let's start with xy terms.
03:11
So we have negative xy on the left and positive xy on the right...