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

1. anonymous

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

2. anonymous

3. zepdrix

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

4. anonymous

1 ——————————— 36 • (x - 5)^3• (x + 1)

5. anonymous

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..

6. anonymous

thats what i got but could be wrong

7. zepdrix

Yes, flip is a good first step!

8. anonymous

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

9. zepdrix

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

10. anonymous

So the signs dont change within the fraction?

11. zepdrix

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

12. anonymous

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

13. zepdrix

Yesss. Stuck on any of those steps? :)

14. anonymous

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

15. zepdrix

k :)

16. anonymous

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

17. anonymous

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..

18. zepdrix

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

19. anonymous

I put that ;p

20. zepdrix

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

21. zepdrix

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

22. anonymous

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

23. zepdrix

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

24. anonymous

Yes (:

25. zepdrix

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?

26. anonymous

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

27. anonymous

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)..

28. anonymous

WOW!

29. anonymous

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

30. anonymous

both* okay*

31. zepdrix

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

32. anonymous

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

33. zepdrix

k brb gonna make a sammich c:

34. anonymous

No problem ;p

35. anonymous

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

36. zepdrix

yayyy good job \c:/

37. anonymous

Thaaank you (: