Question

how would i simplify this?

Answer 1

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

Answer 2

Can you factor y²+y-20?

Answer 3

i woul eliminate the y^2 right?

Answer 4

y^3-20

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

yes

Answer 9

OK, then find these numbers!

Answer 10

(please)

Answer 11

is it 2x/y^2 ?

Answer 12

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

Answer 13

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?

Answer 14

what?

Answer 15

x^2/2y?

Answer 16

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.

Answer 17

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:\[\frac{ y+5 }{ y+3 }\]

Answer 18

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!

Answer 19

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

Answer 20

yw!

Answer 21

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

Answer 22

THIS one is tuff

Answer 23

@andreadesirepen You need to download the file and reupload it on OpenStudy.

Answer 24

@tyteen4a03

Answer 25

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

Answer 26

stay, change, flip?

Answer 27

or do we cross multiply?

Answer 28

@tyteen4a03