Author 
Topic 

moon1130
Senior Member
USA
24 Posts 
Posted  02/04/2013 : 01:16:06

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. 


royhaas
Moderator
USA
3059 Posts 
Posted  02/04/2013 : 08:47:54

What steps have you tried? Your example is the simplest problem possible in partial fractions. 


moon1130
Senior Member
USA
24 Posts 
Posted  02/04/2013 : 11:20:07

I have just started reviewing partial fraction decomposition. I havve done nothing on this problem because I did not know where to start. 


the_hill1962
Advanced Member
USA
1470 Posts 
Posted  02/04/2013 : 11:31:43

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 


moon1130
Senior Member
USA
24 Posts 
Posted  02/04/2013 : 15:06:02

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. 


the_hill1962
Advanced Member
USA
1470 Posts 
Posted  02/04/2013 : 15:59:26

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 11/(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.



moon1130
Senior Member
USA
24 Posts 
Posted  02/04/2013 : 16:33:09

Thank you the_hill1962. Your words were very encouraging.
Have a very Good one... 


royhaas
Moderator
USA
3059 Posts 
Posted  02/05/2013 : 17:14:06

This is exactly why I want students to read their textbooks first. 


moon1130
Senior Member
USA
24 Posts 
Posted  02/05/2013 : 23:59:31

Exccellent point, Royhaas. You are absolutely correct. 



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