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March 31st, 2018, 03:32 AM   #1
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Fractions , linear-algebra!

Hi everyone,

I’m quite new here, so please bare with me!

I’m stuck on a a problem and it’s being consuming my entire day!

The problem is the following

Subtract: x / (x-2).( x+4) from -2 / x^2+2x-8


There are four possible answeres given to me on this problem. They might all be correct or maybe just one of them!

a) -(x+2) / x^2 + 2x - 8

B) -2-x / x^2+2x -8

C) -2-x / (x-2)(x+4)

D) -x-2 / (x-2)(x+4)


I do realize that the denominators are the same, but I’m having trouble figuring out wich options are actually correct( if more than one).

When I try calculating the numerators, with any of the options given ( by substituting x for a given number, all the numerators from the possible answers give me the same result! This leads me to believe that all answers are correct. If I’m wrong, it would be great to understand why!

Thank you so much in advance !!

Last edited by Brunob; March 31st, 2018 at 03:36 AM.
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March 31st, 2018, 04:23 AM   #2
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Quote:
Originally Posted by Brunob View Post
Subtract: x / (x-2).( x+4) from -2 / x^2+2x-8

NOTE: Brackets required:
Subtract: x / ((x-2).( x+4)) from -2 / (x^2+2x-8 )
Let u = x^2 + 2x - 8 = (x-2)(x+4)

-2/u - x/u = (-2 - x)/u = -(x + 2)/u

HOKAY?
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March 31st, 2018, 04:37 AM   #3
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Thanks!!

I think I got what you mean.

So there are 3 correct answers.

Saying u = (x-2)(x+4)=x^2+2x-8


So -(x+2)/ u is correct

-2-x/u is also correct ( that would be B and C)

I’m just not sure why -x-2/u isn’t a correct answer? It does seem to me that it is correct as I would get the same value from others if I put a number for X. Do you mind explaining it to me? Thank u soooo much!
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March 31st, 2018, 04:59 AM   #4
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Quote:
Originally Posted by Brunob View Post
I’m just not sure why -x-2/u isn’t a correct answer?
Isn't that (-x-2)/u ?

If so, then they are ALL correct!

Check by assigning a value to x; say x=10; all 4 choices = -.2

NOTE: make SURE you understand the importance
of proper BRACKETING.

Last edited by Denis; March 31st, 2018 at 05:10 AM. Reason: Add NOTE
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March 31st, 2018, 05:11 AM   #5
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Perfect!

Great! Thank you so much! That’s what I’ve thought!!!

Rgds,
Bruno
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March 31st, 2018, 05:18 AM   #6
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To end this weirdness: do you UNDERSTAND
what I mean with "importance of proper bracketing"?
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April 2nd, 2018, 03:24 PM   #7
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I do!! Thank you very much
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April 4th, 2018, 04:16 AM   #8
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With regard to "the importance of proper bracketing" I would say that NONE of these are correct.
a)$\displaystyle -(x+2) / x^2 + 2x - 8= -\frac{x+ 2}{x^2}+ 2x- 8$ is not correct.

B) $\displaystyle -2-x / x^2+2x -8= -2- \frac{x}{x^2}+ 2x- 8$ is not correct.

C) $\displaystyle -2-x / (x-2)(x+4)= -2- \frac{x}{(x-2)(x+4)}$ is not correct.

D) $\displaystyle -x-2 / (x-2)(x+4)= -x- \frac{2}{(x- 2)(x+4)}$ is not correct.

The correct answer is $\displaystyle -(x+ 2)/(x^2+ 2x- 8 )= -\frac{x+ 2}{x^2+ 2x- 8}= -\frac{x+ 2}{(x- 2)(x+ 4)}$.
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