## anonymous 3 years ago how would i simplify this?

1. anonymous

2. anonymous

First, try to factor both numerator and denominator. If you're lucky, you can then divide out the common factors!

3. anonymous

Can you factor y²+y-20?

4. anonymous

i woul eliminate the y^2 right?

5. anonymous

y^3-20

6. anonymous

No, write it as: y²+y-20=(y ...)(y ...)

7. tyteen4a03

@andreadesirepen y^2 + y != y^3. Different powers.

8. anonymous

On the dots you have to put numbers for which the sum is 1 and the product is -20. Does that sound familiar?

9. anonymous

yes

10. anonymous

OK, then find these numbers!

11. anonymous

12. anonymous

is it 2x/y^2 ?

13. anonymous

No, first you get: y²+y-20=(y-4)(y+5). That is just the numerator.

14. anonymous

Now you have to do the same with the denominator: y²-y-12=(y ...)(y ...) On the dots are now numbers with sum -1 and product -12. What are they?

15. anonymous

what?

16. anonymous

x^2/2y?

17. anonymous

I get the feeling you don't understand what is going on. If I want to factor y²-y-12, which is y² -1*y -12, I must look for two numbers that have sum -1 (the coefficient of y) and product -12 (the constant at the end). These are: -4 and 3. See: -4*3 = -12, -4+3 = -1. Why does this work? Try it: (y -4)(y+3) can be expanded again, using FOIL: First: y*y = y² Outer: y*3 = 3y Inner: -4*y = -4y Last: -4*3 = -12 Together, this becomes: y² +3y-4y-12 = y²-y-12. So you have to look at it like: y² +(a+b)y + ab = (y+a)(y+b) That is why you say: the sum is the number befor the y the product is the number at the end.

18. anonymous

So after all this factoring, we now have:$\frac{ y^2+y-20 }{ y^2-y-12 }=\frac{ (y+5)(y-4) }{ (y+3)(y-4) }$ Only now is the moment we can simplify! Because only now we have a product in the numerator and also a product in the denominator. Both products have x-4 as a common factor. That can therefore be divided out, leaving only:$\frac{ y+5 }{ y+3 }$

19. anonymous

So, I'm sorry, but there is no quick way to just mess a bit with the numbers in your original fraction :( What you have to do (always!) is: 1. write numerator as a product (=factor it) 2. write denominator as a product (=factor it) 3. Look for common factors. Divide them out. 4. See what is left. This is your answer!

20. anonymous

it´ll take me a while to figure this. thanks though!

21. anonymous

yw!

22. anonymous

do you know this one ? http://learn.flvs.net/webdav/assessment_images/educator_algebra2_v10/09_14_31.gif

23. anonymous

THIS one is tuff

24. tyteen4a03

25. anonymous

26. anonymous

@tyteen4a03

27. tyteen4a03

@andreadesirepen Same drill. Remember that this expression can also be written as $$\frac{12x}{x^2+6x+9} \times \frac{x^2-9}{4x^2}$$.

28. anonymous

stay, change, flip?

29. anonymous

or do we cross multiply?

30. anonymous

@tyteen4a03