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 Algebra
 Partial Fraction Decomposition
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moon1130
Senior Member

USA
24 Posts

Posted - 02/04/2013 :  01:16:06  Show Profile  Reply with Quote
Hi,

I have been having trouble performing partial fraction decomposition on x/(x+1). Could someone show me each step on how it is done?

Thank you.
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royhaas
Moderator

USA
3059 Posts

Posted - 02/04/2013 :  08:47:54  Show Profile  Reply with Quote
What steps have you tried? Your example is the simplest problem possible in partial fractions.
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moon1130
Senior Member

USA
24 Posts

Posted - 02/04/2013 :  11:20:07  Show Profile  Reply with Quote
I have just started reviewing partial fraction decomposition. I havve done nothing on this problem because I did not know where to start.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 02/04/2013 :  11:31:43  Show Profile  Reply with Quote
royhaas, could you tell us a little more than this is the "simplest problem"?
I don't find it to be the simplest.
Now, something like
(3x+2)/(x+x) is simple to do.
What I don't understand (and possibly the same thing moon1130 doesn't either) is:
Both the numerator and the denominator are linear in x/(x+1) .
I mean, what would you factor "x+1" into?
Isn't that one of the steps in decompostion (to factor the denominator)?
Maybe this problem is SO simple that I don't get it.
Are we supposed to get an answer of the form
A/x + B/(x+1) or what?


Edited by - the_hill1962 on 02/04/2013 11:41:55
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moon1130
Senior Member

USA
24 Posts

Posted - 02/04/2013 :  15:06:02  Show Profile  Reply with Quote
I have reviewed partial fraction decomposition from this site and from other sites.

The rational expression being worked on must be a proper fraction. That is, the degree of the denominator must be larger than the degree of the numerator. If the rational expression is an improper fraction, i.e., the degree of the numerator is equal to or larger than the degree of the denominator, then you must use long division and divide the denominator into the numerator. The result will be whole number Remainder, C r(x)/d(x), where C is a constant, R(x) is the remainder, and d(x) is the denominator.

X/(x+1) is an improper fraction. Therefore, we do the long division.

x(x+1) = 1- 1/(x+1).

Royhaas or someone else will have to tell me if the problem is correct and complete.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 02/04/2013 :  15:59:26  Show Profile  Reply with Quote
Yes, you have it correct. Excellent!
I had forgotten that long division is used when it is an improper fraction.
The decomposition of x/(x+1) is 1-1/(x+1)
Nice work.

quote:
Originally posted by moon1130

I have reviewed partial fraction decomposition from this site and from other sites.

The rational expression being worked on must be a proper fraction. That is, the degree of the denominator must be larger than the degree of the numerator. If the rational expression is an improper fraction, i.e., the degree of the numerator is equal to or larger than the degree of the denominator, then you must use long division and divide the denominator into the numerator. The result will be whole number Remainder, C r(x)/d(x), where C is a constant, R(x) is the remainder, and d(x) is the denominator.

X/(x+1) is an improper fraction. Therefore, we do the long division.

x(x+1) = 1- 1/(x+1).

Royhaas or someone else will have to tell me if the problem is correct and complete.

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moon1130
Senior Member

USA
24 Posts

Posted - 02/04/2013 :  16:33:09  Show Profile  Reply with Quote
Thank you the_hill1962. Your words were very encouraging.

Have a very Good one...
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royhaas
Moderator

USA
3059 Posts

Posted - 02/05/2013 :  17:14:06  Show Profile  Reply with Quote
This is exactly why I want students to read their textbooks first.
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moon1130
Senior Member

USA
24 Posts

Posted - 02/05/2013 :  23:59:31  Show Profile  Reply with Quote
Exccellent point, Royhaas. You are absolutely correct.
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