Question

Algebra equation! simplify completely (x^2 + x - 12) / (x^2 - x - 20) divided by (3x^2 -24x + 45) / (12x^2 - 48x - 60)

Answer 1

@adrynicoleb @Ahsome @amydh @bebe365 @badboy18 @ChrystalC @CoconutJJ @Chelsey2015 @ChiakiNagoya @camman I'll award a medal!

Answer 2

@Luigi0210 @zepdrix please help

Answer 3

\[\large\rm \frac{x^2 + x - 12}{x^2 - x - 20}\div\frac{3x^2 -24x + 45}{12x^2 - 48x - 60}\]We gotta simplify huh? :)
So I guess we'll need to do some good ole factoring.

Answer 4

1
———————————
36 • (x - 5)^3• (x + 1)

Answer 5

Well, dont we first flip the second fraction and switch the sign to multiplication? I just cant remember if we change the signs within the fraction when we flip it..

Answer 6

thats what i got but could be wrong

Answer 7

Yes, flip is a good first step!

Answer 8

@yinkim52001 Thanks so much for trying to help! But I want to learn how to do this as I am struggling with the problem (:

Answer 9

\[\large\rm \frac{x^2 + x - 12}{x^2 - x - 20}\cdot\frac{12x^2 - 48x - 60}{3x^2 -24x + 45}\]

Answer 10

So the signs dont change within the fraction?

Answer 11

correct. no change.
example:\[\large\rm \frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}=\frac{a}{b}\cdot\frac{d}{c}\]This is how we apply this "flip" idea ^
See how nothing changed to negative? :o

Answer 12

Yes! So what is the next step? I factor both denominators and both numerators?

Answer 13

Yesss.
Stuck on any of those steps? :)

Answer 14

Not yet! Lol I have to try it out. Will you please give me a minute?

Answer 15

k :)

Answer 16

Okay! So I have (x-3)(x+4) / (x-4)(x+5) times 12(x^2 - 4x -5) / 3(x^2 - 8x + 15)

Answer 17

I'm not sure how to further factor the right fraction because the top has a prime number (5) and the denominator is giving me an issue too..

Answer 18

\[\large\rm \frac{(x-3)(x+4)}{\color{red}{(x-4)(x+5)}}\cdot\frac{12(x^2-4x-5)}{3(x^2-8x+15)}\]Woops! :O
Double check the red a sec.
Rest looks good though.

Answer 19

I put that ;p

Answer 20

ya it's incorrect! :O fix it silly!

Answer 21

The middle term is negative,
so the LARGER number should get the negative sign, ya? :)

Answer 22

I guess it would have to be (x + 4) and (x - 5) haha

Answer 23

\[\large\rm \frac{(x-3)(x+4)}{(x+4)(x-5)}\cdot\frac{12(x^2-4x-5)}{3(x^2-8x+15)}\]Ooooo kay great!

Answer 24

Yes (:

Answer 25

You are correct about the 5 being prime.
Which means, IF IT CAN FACTOR, the only options we have will be 1 and 5, ya?

Answer 26

Ohhh! Right, I didn't even think about that for some reason ;p Let me try to factor further!

Answer 27

Okay so that would factor out to (x - 5) (x + 1), but I tried factoring out the denominator and I couldn't figure it out because neither (x + 5)(x - 3) nor (x + 3)(x - 5) were foiling out to be (x^2 - 8x + 15)..

Answer 28

WOW!

Answer 29

Just realized they could noth be negative... Okat my bad

Answer 30

both* okay*

Answer 31

ya there ya go :) same sign since the 15 is positive

Answer 32

Right! So let me see what I can do this far & I'll come back with my answer or if I get stuck ;p

Answer 33

k brb gonna make a sammich c:

Answer 34

No problem ;p

Answer 35

Got it!!! It's 4(x+1) / x - 5 Thank you so so much! <3

Answer 36

yayyy good job \c:/

Answer 37

Thaaank you (: