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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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