1
00:00:00,867 --> 00:00:07,105
We've got... All of that divided by

2
00:00:07,105 --> 00:00:09,400
4xy

3
00:00:09,400 --> 00:00:12,533
There are several ways to think about them, they're all equivalent

4
00:00:12,533 --> 00:00:15,400
This is going to be the exact same thing. We can esssentialy sort of separate the numerators.

5
00:00:15,400 --> 00:00:34,667
This is the same thing as...

6
00:00:34,667 --> 00:00:36,333
And there's multiple ways to think about it.

7
00:00:36,333 --> 00:00:40,000
One is: If I have a+b over c

8
00:00:40,000 --> 00:00:43,800
this is clearly the same thing as a over c plus b over c

9
00:00:43,800 --> 00:00:46,933
we're just adding the--we're taking the fraction apart.

10
00:00:46,933 --> 00:00:49,691
If we did it in reverse, we'd just be adding fractions

11
00:00:49,691 --> 00:00:51,400
Another way to think about it is

12
00:00:51,400 --> 00:00:52,600
We're distributing the division.

13
00:00:52,600 --> 00:00:56,000
We're dividing the whole thing by 4xy

14
00:00:56,000 --> 00:00:58,096
so we divide each of the terms by 4xy.

15
00:00:58,096 --> 00:01:00,349
The last way to think about it, which is really the same thing,

16
00:01:00,349 --> 00:01:04,087
is that we're multiplying the whole thing by 1 over 4xy

17
00:01:04,087 --> 00:01:07,600
So we're distributing the 1 over 4xy times everything

18
00:01:07,600 --> 00:01:10,800
which is the same as dividing by 4xy.

19
00:01:10,800 --> 00:01:13,667
Either way we get to this and we just have to simplify this

20
00:01:13,667 --> 00:01:15,867
really just using exponent properties.

21
00:01:15,867 --> 00:01:20,867
So we can divide 12. 12 divided by 4 is pretty straight forward

22
00:01:20,867 --> 00:01:25,267
that is just 3, so let me just write it this way.

23
00:01:25,267 --> 00:01:30,400
So 12 divided by 4 is 3. And x squared

24
00:01:30,400 --> 00:01:35,434
divided by x. Remember x is the same thing as x to the first power,

25
00:01:35,434 --> 00:01:39,846
so thats going to be x to the three minus two

26
00:01:39,846 --> 00:01:45,200
Sorry, x to the three minus one power.

27
00:01:45,200 --> 00:01:52,013
Which would be x squared. And finally

28
00:01:52,013 --> 00:01:54,533
you have y to the third divided by y.

29
00:01:54,533 --> 00:01:57,098
Well thats just divided by y to the one.

30
00:01:57,098 --> 00:02:01,022
and y to the third divided by y to the one is going to be y squared.

31
00:02:01,022 --> 00:02:03,267
Three minus one is two.

32
00:02:03,267 --> 00:02:05,733
Now lets do the next term.

33
00:02:05,733 --> 00:02:13,267
Plus, we have sixteen over 4, which is just four.

34
00:02:13,267 --> 00:02:18,925
That is just equal to four. Then we have x to the fourth over

35
00:02:18,925 --> 00:02:23,733
x. Well, once again, x is just the same thing as x to the first

36
00:02:23,733 --> 00:02:28,840
So this is going to be x to the four minus one or x to the third power.

37
00:02:28,840 --> 00:02:33,133
And then finally, we have y divided by y.

38
00:02:33,133 --> 00:02:34,733
Well, thats just going to be one.

39
00:02:34,733 --> 00:02:39,133
So we don't even have to write it down. We could right one here,

40
00:02:39,133 --> 00:02:40,682
but that wont do much, won't change the values.

41
00:02:40,682 --> 00:02:43,400
So just these guys essentially cancel out. And then finally you have

42
00:02:43,400 --> 00:02:48,800
ten divided by 4. they're both divisible by two, so it becomes five halves.

43
00:02:48,800 --> 00:02:53,523
So that part over there simplifies to five over two.

44
00:02:53,523 --> 00:02:58,533
So, plus five halves and then x divided by x.

45
00:02:58,533 --> 00:03:01,867
Those just cancel out, so thats just one.

46
00:03:01,867 --> 00:03:03,533
y divided by y, thats just one as well.

47
00:03:03,533 --> 00:03:05,133
So we're left with five halves.

48
00:03:05,133 --> 00:03:06,015
And we're done!

49
00:03:06,015 --> 99:59:59,999
This whole expression simplified to...