1
00:00:00,667 --> 00:00:03,097
simplify the expression 18x to the fourth

2
00:00:03,097 --> 00:00:04,690
minus 3x squared

3
00:00:04,690 --> 00:00:06,971
plus 6x minus 4, all of that over 6x

4
00:00:06,971 --> 00:00:10,789
so theres a couple ways to think about it

5
00:00:10,789 --> 00:00:12,173
there all really equivalent

6
00:00:12,173 --> 00:00:16,087
you really just view this up here as being the exact same thing

7
00:00:16,087 --> 00:00:20,906
as 18x to the fourth over 6x

8
00:00:20,906 --> 00:00:23,817
plus negative 3x squared over 6x

9
00:00:23,817 --> 00:00:28,086
or you could say minus 3x squared

10
00:00:28,086 --> 00:00:32,290
over 6x plus 6x over 6x

11
00:00:32,290 --> 00:00:33,709
minus 4 over 6x

12
00:00:33,709 --> 00:00:35,371
now theres a couple ways to think about it

13
00:00:35,371 --> 00:00:36,857
one is

14
00:00:36,857 --> 00:00:38,424
I just kind of decomposed this numerator

15
00:00:38,424 --> 00:00:40,400
up here, if I just had a buch of stuff

16
00:00:40,400 --> 00:00:43,219
a+b+c over d

17
00:00:43,219 --> 00:00:46,876
thats clearly equal to A over D plus B over D

18
00:00:46,876 --> 00:00:49,287
plus C over D

19
00:00:49,287 --> 00:00:52,999
or maybe not so clearly but hopfully tht helps clarify but

20
00:00:52,999 --> 00:00:54,320
another way to think about it is kind of like

21
00:00:54,320 --> 00:00:55,759
your distributing the division

22
00:00:55,759 --> 00:00:59,717
if I divide a whole expression by something thats

23
00:00:59,717 --> 00:01:02,725
equivalant to dividing each of the terms by that something

24
00:01:02,725 --> 00:01:08,808
Another way to think about it is that were multiplying this entire expresion

25
00:01:08,808 --> 00:01:11,619
so this is the same thing as one over 6x

26
00:01:11,619 --> 00:01:13,908
times these entire thing

27
00:01:13,908 --> 00:01:15,754
times 18x to the fourth-3x squared

28
00:01:15,754 --> 00:01:23,095
plus 6x minus 4 and so here this would be just the straight distributive property.