Rational Expressions

A

adr8

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Aug 1, 2011
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I want to know if I got the answer right. My problem is (x+1)2(x+2)3-(x+1)3(x+2)2/(x+2)6

(x+1)2(x+2)2[x+2-x-1]/(x+2)6

(x+1)2(x+2)2(1)/(x+2)6


I followed the process of elimination by elimination (x+2)^2 and in the demonitor instead of ending with (x+2)^6 I ended up with (x+2)^4 as my denominator.

(x+1)2/(x+2)4=Answer
 
Sorry for the late reply but thanks once again. There are two problems that I was wondering if I have right. I uploaded the attachment. When you see the attachment there should be a line between the 6x.... and (x^3+2)^6. I will put the other one in a little bit.
 

Attachments

  • 1.txt
    264 bytes · Views: 5
Code: 
6x(x^2+1)^2(x^3+2)^3-9x^2(x^2+1)^3(x^3+2)^2
-------------------------------------------
                (x^3+2)^6


3x(x^2+1)^2(x^3+2)^2[2(x^3+2)-3x(x^2+1)]
----------------------------------------
              (x^3+2)^6


3x(x^2+1)^2(x^3+2)^2[2x^3+4-3x^3-3x)]
-------------------------------------
            (x^3+2)^6


3x(x^2+1)^2[COLOR=#0000ff]-x^3-3x+4[/COLOR]
--------------------
     (x^3+2)^4


The part in blue is a factor; it should be enclosed in grouping symbols.

I examined only your result; I used software (MVR5) to confirm it.

MVR5 shows the following, which is equivalent to your result.

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



In the future, please do not attach text files. Cut-and-paste your text directly into your post, instead.

I drew the "fraction bars" using the [ Code ] tags.
 
Code: 
1         minus    1                          (x^2) 1        minus   1    (x+y)^2
(x+Y)^2            x^2                        (x^2)(x+y)^2          (x^2) (x+y)^2
            Y                                                 Y

x^2-(x+y)^2                                     (x^2)-(x+y)(x+y)=x^2-(x^2+2xy+y^2)
(x^2)(x+y)^2                                              (x^2)(x+y)^2
     
     Y                                                         Y

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

Your text file is not easy to understand. I'm thinking that the given expression is the following.

\(\displaystyle \frac{\frac{1}{(x + Y)^2} - \frac{1}{x^2}}{Y}\)

If so, then your result is not correct.

Compare your denominators above in the next-to-the-last line and your result. You dropped an exponent, in your result.

Also, you could factor -1 out of the numerator.

Note: do not interchange symbols Y and y. These are different symbols; they do not mean the same thing, so stick with one or the other.

Finally, we prefer that you start a new thread for each new exercise that you want to discuss.
 
Last edited:
Thanks, I will try to use substitutions next time though lol. I can understand about the headache thing cause honestly I think this is a new method that they are showing us in the book because I dont remember using this method lol.

As for the second problem, yea thats how the problem looks. Sorry about that. The reason why I did the attachments is because I didnt know how to put them as a fraction on here lol. I tried using it on the attachment but I noticed it didnt let me but I will try to use the code. I think the last post you mentioned is the code right?

So as far the second problem goes, I was doing it correctly till the seccond to the last step?
 
Last edited:
adr8 said:
The reason why I did the attachments is because I didnt know how to put them as a fraction on here lol.

I understand, but your text file does not show fractions, either. So, you gained nothing by using those text-file attachments.

You don't need to "draw" fractions, regardless. We text these types of expressions using grouping symbols around numerators and denominators. Like this:

[1/(x + Y)^2 - 1/x^2]/Y

Also, if you're interested in learning about LaTex math formatting, you can double-click any LaTex expression in a post, and a pop-up window will show how it was coded.

Try double-clicking this one:

\(\displaystyle \frac{\frac{1}{(x + Y)^2} - \frac{1}{x^2}}{Y}\)


I think the last post you mentioned is the code right?

No. I mentioned the code tags in the post previous to that one. If you click the [Reply with quote] button in that post, then you can see how I coded it. After you're done looking at the code, hit your backspace key to return.


So as far the second problem goes, I was doing it correctly till the seccond to the last step?

Yes. Your second-to-the-last result on the third exercise is correct. (I did not look at the intermediate steps.)

Your answer does not show the exponent on x^2.
Click to expand...

This thread is a good example of why we should not try discussing three different exercises within one thread. The discussion has become confusing. Please start a new thread for each new exercise. Cheers!
 
Last edited:
I see what you mean. Do you want me to start a new thread on the one that I was asking you about? I was referring to the exercise in which I posted the second attachment on.
 
Yes, starting a new thread is probably a good idea. You can copy-and-paste from this thread to the new one.
 
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