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Find all Integer Values of x....


Date: 6/27/96 at 22:39:33
From: Anonymous
Subject: Find all Integer Values of x....

Dr. Math,

Find all integer values of x for which [12(x^2-4x+3) / (x^3-3x^2-x+3)]  
has a positive integer value.

Thank you,
       Richard


Date: 6/28/96 at 13:40:21
From: Doctor Tracy
Subject: Re: Find all Integer Values of x....

Richard,

The first thing that you need to do in this problem is to factor both 
the numerator and denominator of this fraction completely.  At this 
point make sure to rule out any values of x which make the denominator 
0.  Now, you should be able to cancel some of the factors to end up 
with a numerator of 12 and a linear expression in x for the 
denominator.  

Since you want to know which values of x give you a positive integer 
value for the expression, you now know that you want the denominator 
of the reduced expression to be a positive divisor of 12. That is, the 
denominator must equal 1, 2, 3, 4, 6 or 12.  Solve for x in each of 
these cases and you will have your answers. Make sure not to include 
the values that you ruled out earlier.  

I'm pretty sure you can complete the problem now.  I hope this helps.

-Doctor Tracy,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra

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