Rational Expressions 2

[adr8]

[1/(x + Y)^2 - 1/x^2]/Y This is the original problem



(x^2)__1___ - _1_ (x+y)^2
(x^2) (x+y)^2 (x+y)^2
___________________________
y


x^2-(x+y)^2
_____________
(x^2)(x+y)^2
_______________
y


x^2-(x+y)(x+y)
______________
(x^2)(x+y)^2
__________________
y


x^2-x^2-2xy-y^2
______________________
(x^2)(x+y)^2
____________________
y


-2xy-y^2
_____________
(x^2)(x+y)^2
__________
y


-2xy-y^2 * (1/y)
__________
(x^2)(x+y)^2

-2xy-y^2
_____________
(x^2 y)(x+y)^2



My answer is
-2-y^2
x(x+y)^2

 

[mmm4444bot]

-2xy-y^2 -2xy-y^2 times 1
(x^2)(x+y)^2 (x^2)(x+y)^2 y
Y

Look at the factor x^2 highlighted in red in your denominator above.

Then look at the denominator in your answer below.

I told you about this mistake, in your other thread. You have not yet fixed this mistake.

My answer is

  -2-y^2
----------
 x(x+y)^2

We also factor out -1, when all of the terms are negative, like in the numerator above.

Did you notice what happened when you spaced stuff without enclosing the whole thing within

 tags?

It looks like garbage because this site strips out repeated word spaces. Put your "drawing" inside the code tags, to prevent the removal of extra spaces. I'm thinking that I already told you this, but perhaps you don't understand what I meant by code tags. If so, and you would like to understand, all you need do is ask.


By the way, if you click the [Preview Post] button before posting, you will see exactly how your typing will render. That allows you to fix issues before posting.


(I still think it's easier to type rational expressions using grouping symbols versus trying to "draw" them with the space bar.)

 

[adr8]

Yea I noticed, its just that I was fixing it before you read it lol.

 

[mmm4444bot]

OIC.

That happens, sometimes.

By the way, it would be better if the composition window here used a fixed-width font because, even when your "drawing" looks correct in the composition window, stuff within the code tags has issues with things not lining up.

I usually "draw" my drawings in Notepad using the Courier (or New Courier) font because it is a fixed-width font. In other words, what you see is what you get. After the drawing is aligned and spaced how I want it in Notepad, I then copy-and-paste it into the composition window here -- enclosing it in code tags.

This saves me the time and effort of counting spaces or characters and repeatedly previewing/adjusting to get it right.

(It is simply easier to use grouping symbols.)

 

[adr8]

Oh ok, I think know what you mean. I was trying to do it but it didnt come out. I dont think I did it right.

Going to the problem would my answer look lik this -1(y^2+2)/x(x+y)^2

 

[adr8]

A lot of your graphic work can be eliminated.

Let u = (x + Y).

Then your expression simplifies to [(1 / u²) - (1 / x²)] / Y, which is much easier to work with. Even this expression gets a little hairy to work with, but you are far less likely to err than with the original.

I think your answer is wrong.

[(1 / u)²- (1 / x)²] / Y =

[(1 / u)² - (1 / x)²] / Y =

{[(1 / u) - (1 / x)] * [(1 / u) + (1 /x)]} / Y =

{[(x - u) / ux] * [(x + u) / ux]} / Y =

[(x² - u²) / (ux)²] / Y =

{[x² - (x² + 2xY + Y²) / (ux)²} / Y =

[-(2xY + Y²)/ (ux)²] / Y =

-(2x + Y) / (ux)² =

-(2x + Y) / [x²(x + Y)²]

I got confused on the colored part. Why do we add this part [(1 / u) + (1 /x)]} to the expression?

 

[adr8]

Okay, I was reviewing it and yea it makes sense now.

 

[adr8]

A lot of your graphic work can be eliminated.

Let u = (x + Y).

Then your expression simplifies to [(1 / u²) - (1 / x²)] / Y, which is much easier to work with. Even this expression gets a little hairy to work with, but you are far less likely to err than with the original.

I think your answer is wrong.

[(1 / u)²- (1 / x)²] / Y =

[(1 / u)² - (1 / x)²] / Y =

{[(1 / u) - (1 / x)] * [(1 / u) + (1 /x)]} / Y =

{[(x - u) / ux] * [(x + u) / ux]} / Y =

[(x² - u²) / (ux)²] / Y =

{[x² - (x² + 2xY + Y²) / (ux)²} / Y =

[-(2xY + Y²)/ (ux)²] / Y =

-(2x + Y) / (ux)² =

-(2x + Y) / [x²(x + Y)²]

As I was reviewing this problem, I have two questions. In the following red parts:

1. I can see how you got [(x² - u²) / (ux)²] / Y , since we have x-u on one side while x+u on the other side, why dont we combine them first before factoring? Also, is that allowed in math to factor them like that [(x² - u²) / (ux)²] / Y without combining them? In other words since u=x+y why is it that dont we combine them together like this x-(x+y)= -y while on the other side would be x+(x+y)= 2x+y and then factor? Just wondering....

2. My next question is I know the I know the y in the denominator cancels out with the 2xy, but how come we have y instead of y² , since we only have one y as our denominator?