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 Accuplacer test Elementry algebra Q's
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krazykay3224
Junior Member

USA
4 Posts

Posted - 10/14/2011 :  14:51:37  Show Profile  Reply with Quote
6.
X > 2, then (x^2-x-6)/ (x^2-4)

A. (x-3)/(2)
B. (x-3)/(x-2)
C. (x-3)/(x+2)
D. 3/2



I have the key and Answer is B. But that is not helping me. Please break this down into math for dummies style. This is the site I got the review from http://www.collegeboard.com/student/testing/accuplacer/preparation-sample.html . Thank you.
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 10/14/2011 :  18:34:05  Show Profile  Reply with Quote
(x^2-x-6)/ (x^2-4) = (x-3)(x+2)/[(x+2)(x-2)] = (x-3)/(x+2), since x > 2, x - 2 has been cancelled.

Therefore, the answer is B.
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 10/15/2011 :  17:26:09  Show Profile  Reply with Quote
Just a comment about the word "cancel". When something cancels in the mathematical sense, it means the result is zero. What you mean here is to "divide out". I know that many students (and teachers) use cancel to mean this process but that is incorrect.
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krazykay3224
Junior Member

USA
4 Posts

Posted - 10/15/2011 :  19:01:34  Show Profile  Reply with Quote
Ok. I had done research on the problem on yahoo and was able to see the break down, but I am not understanding the reasoning. What I am asking is for someone to explain it.. not just write it out... i apologize if i did not express this in my last post... First what is this method or type of math called? Also can you please explain step by step what the reason is that these things are being done. Are we dividing -6 by 2 to get -3 and then dividing -4 by 2 to get -2 and then just moving the positive 2, or is this factoring all the numbers are divisible by 2. Can you please explain it as if you were having to teach it to someone that has no experience. Thank you-
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 10/15/2011 :  20:00:50  Show Profile  Reply with Quote
quote:
Originally posted by Ultraglide

Just a comment about the word "cancel". When something cancels in the mathematical sense, it means the result is zero. What you mean here is to "divide out". I know that many students (and teachers) use cancel to mean this process but that is incorrect.


I did some search and found out word 'cancel' in Mathematics means:
"To remove (a common factor) from the numerator and denominator of a fractional expression.
To remove (a common factor or term) from both sides of an equation or inequality."

http://www.answers.com/topic/cancel


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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 10/15/2011 :  23:36:43  Show Profile  Reply with Quote
With all due respect, I disagree with the result that you found. As I said before cancel means to combine to give zero. By dividing out a common factor you do not get zero.
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TchrWill
Advanced Member

USA
79 Posts

Posted - 10/16/2011 :  09:40:24  Show Profile  Reply with Quote
(x^2-x-6) is equivalent to
(x^2-4)

(x-3)(x+2)
[(x-2)(x+2)]

(x+2) being common to both numerator and denominator
(x+2)divided by (x+2) = 1 resulting in

(x-3)(1)
[(x-2)] or

(x-3)
[(x-2)]

If x > 2, then b is the correct answer.
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krazykay3224
Junior Member

USA
4 Posts

Posted - 10/16/2011 :  20:56:55  Show Profile  Reply with Quote
Thank you
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 10/19/2011 :  11:31:57  Show Profile  Reply with Quote
Ultraglide: I don't understand your limited definition of cancel either. True, cancel can mean "combine to get zero" but it can also mean to "divide out to get one".
http://www.definitions.net/definition/cancel
I would be interested in looking at where you get your limited definition from. Do you have a particular site or reference book that you are using?
About the use of the word "cancel" by students and teachers; why is it incorrect? I tend to avoid the use of the word and do use the phrase "divide out" or "subtract out" but "cancel" can be used for both instances.
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 10/19/2011 :  12:14:40  Show Profile  Reply with Quote
When you divide out, you get one, when you cancel, you get zero. As far as the linked web site, I have found at least one that does not make the reference to division:

http://www.ldoceonline.com/dictionary/cancel

Many of sites that do make a reference to division seem the have the same statement.
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