Question

how do you simplify (18u^6v^5+24u^3v^3)/42u^2v^5

Answer 1

Try factoring the top first. Factor out all the numbers, u, and v terms you can. Then look for opportunities to cancel with the terms on the bottom.

Answer 2

ok i factored out the top but i still dont know what to do next..

Answer 3

what did you get?

Answer 4

3u^3v^3(6u^3v^2+8) / 42u^2v^5

Answer 5

ok, great

Now you can cancel the 3 with the 42... 3 "goes into" 42 by 14

Answer 6

so 14 is left on bottom

and you can cancel the u^2 on the bottom with the u^3 in the front on top, leaving just u out front

and cancel the v^3 out in front on top with the v^5 on the bottom, leaving v^2 on the bottom

Answer 7

alright so what to i do with (6u^3v^2+8)?

Answer 8

Hold on...
Is (18u^6v^5+24u^3v^3)/42u^2v^5
written like:
\[\frac{ 18u ^{6}6v ^{5}+24u ^{3}v ^{3} }{ 42u ^{2}v ^{5} }\]

Answer 9

yup

Answer 10

You can simplify that part in your last post slightly by multiplying the 6 and 3 together to get (18u^3v^2 + 8) and you could then factor out another 2, to get 2(9u^3v^2 + 4), but you can't cancel that 2 with anything on the bottom because you only had 13 left on the bottom.

Answer 11

you mean 14 on the bottom..

Answer 12

so like you had,
3u^3v^3(6u^3v^2+8) / 42u^2v^5

simplify parenthesis and factor out 2 to get:
(3u^3v^3)(2)(9u^3v^2 + 4) / 42u^2v^5

and cancel whatever you can to get:

2u(9u^3v2 + 4) / 13v^3

Answer 13

yes, sorry, 14 on bottom

Answer 14

so you CAN cancel that extra 2 on top, leaving 7 on the bottom

Answer 15

good catch!

Answer 16

alright so now we got rid of the 2 and then put the 7 on the bottom, i then factored the u(9u^3v^2+4) and simplified the v's and got (9u^3+4u)/7....

Answer 17

you lost me... but I also messed up... I multiplied the 6 and 3 inside the parenthesis to get 18, but then when I factored out the 2 (to leave 9), I left the original 3 in the term :( Sorry

Answer 18

wait, hold on, that 3 was the exponent on u. typing this stuff is killing me... sorry for the confusion.

Answer 19

Should be:
2u(9u^3v^2 + 4) / 14v^3

Then cancel the 2:

u(9u^3v^2 + 4) / 7v^3

An you are done at that point... all simplified.

Answer 20

Ugly, yes, but simplified

Answer 21

ya i tried to go a step further but i will leave at that this is complicated enough. thank u so much!