Very Confused: Division of Polynomials and Factoring

[colormekaylee]

The Orginial Problem is :

(3x+3y+3 )/(9x ) ÷ (x^2+ 2xy+y^(2 )-1)/(x^4- x^2 ) ( It looked alot better on word)

I know that to start, you need to flip the second problem so it would look like this :

(3x+3y+3 )/(9x ) x (x^4- x^2 )/ (x^2+ 2xy+y^(2 )-1)

I have had trouble getting any further, I put the problems together, but when it gets to the point of factoring them i am completley lost, so basically im here:

(3x+3y+3)(x^4- x^2 )
(9x)(x^2+ 2xy+ y^(2) - 1)

Where do I go from here?

 

[Deleted member 4993]

The Orginial Problem is :

(3x+3y+3 )/(9x ) ÷ (x^2+ 2xy+y^(2 )-1)/(x^4- x^2 ) ( It looked alot better on word)

I know that to start, you need to flip the second problem so it would look like this :

(3x+3y+3 )/(9x ) x (x^4- x^2 )/ (x^2+ 2xy+y^(2 )-1)

I have had trouble getting any further, I put the problems together, but when it gets to the point of factoring them i am completley lost, so basically im here:

(3x+3y+3)(x^4- x^2 )
(9x)(x^2+ 2xy+ y^(2) - 1)

Where do I go from here?

\(\displaystyle \frac{\frac{3x+3y+3}{9x}}{\frac{x^2+2xy+y^2-1}{x^4-x^2}}\)

\(\displaystyle = \frac{3x+3y+3}{9x} \cdot \frac {x^4-x^2}{x^2+2xy+y^2-1}\)

\(\displaystyle = \frac{x+y+1}{3x} \cdot \frac {x^2(x^2 - 1^2)}{(x+y)^2 - 1^2}\)

Now continue with further factirization and cancellation of common factors.....

 

[colormekaylee]

I cant fiqure out what would cancel out after that. I think the 1^2 would and maybe the x + y, but im not sure, would it go any further than that?

 

[mmm4444bot]

You are not ready to attempt exercises like this one.

(I mean, somebody was responsible for teaching you basic factoring patterns and only a few special factoring patterns, before assigning an exercise like this.)

x^2 - 1^2 is called a difference of squares because one square is being subtracted from another square. Any expression that presents as a difference between two squared objects can always be factored the same way!

A^2 - B^2 = (A + B)*(A - B)

c^2 - d^2 = (c + d)*(c - d)

z^2 - 16 = (z + 4)*(z - 4)

9m^2 - 121n^2 = (3m)^2 - (11n)^2 = (3m + 11n)*(3m - 11n)

So, what do you think about the following, now?

x^2 - 1 = (????)*(????)

(x + y)^2 - 1 = (????)*(????)

 

[colormekaylee]

Yea, I have no idea, you just confused me more. No specific person was responsible for teaching me this, I take my school online, so the only thing I have to go off of is example from the book. There are no examples like this in book which is why I am confused and am asking for help here.

I dont understand what you were trying to show me, I just know that the problem I have dosen't make since, and I want to fiqure out the problem, not other stuff that isint it .

 

[stapel]

Yea, I have no idea...

I dont understand what you were trying to show me, I just know that the problem I have dosen't make since, and I want to fiqure out the problem, not other stuff that isint it .

But, as was explained, you need that "other stuff that isn't it" in order to "make sense" of this exercise. You need the pre-requisite content. Unfortunately, this conceptual foundation seems to be missing, which means you need to study a few weeks' or months' worth of material in order to be able to understand what this question is asking.

Please think seriously about hiring a qualified local tutor, and setting aside a few hours a week for intensive private lessons. By working with you face-to-face, your tutor can try to find the gaps in your background which are preventing you from learning the new material, and then provide you with customized instruction to help you get caught up with the course.

My best wishes to you in your studies.

 

[mmm4444bot]

I take my school online

There's the problem, in a nutshell.

Machines teaching the clueless is tantamount to the blind leading the blind.

If you're serious about becoming educated, then find some human teachers.

If this is not acceptable to you, then can you at least recognize what you don't understand from the machines sufficiently to come back here and ask specific questions regarding these online lessons?

It seems to me that the machines had responsibility to teach you about a difference of squares BEFORE asking you to complete the exercise in this thread.

Cheers

 

[whitecanvas]

hi there,

i'm an independent study student, too. when i started, coolmath.com was very helpful for me. still is. when i forget something, always refer back to it. you should try going there and follow through all the lessons for algebra and then follow it along with your textbook. purplemath was helpful too.

for me, when i don't get something, i would avoid it for a day or two. After that, I get back to it, and then it would slowly start clicking for me. hope it helps. just stay focus and you should be fine. good luck.

Abby

 

[Deleted member 4993]

hi there,

i'm an independent study student, too. when i started, coolmath.com was very helpful for me. still is. when i forget something, always refer back to it. you should try going there and follow through all the lessons

And there is the solution .... hard work. Whether on-line or off-line do all the problems you can see - till and untill you can do those in your head.

for algebra and then follow it along with your textbook. purplemath was helpful too.

for me, when i don't get something, i would avoid it for a day or two. After that, I get back to it, and then it would slowly start clicking for me. hope it helps. just stay focus and you should be fine. good luck.

Abby