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avatar+1477 

Hey guys and gals. l've returned to the forum! And with my return comes along a confidence harder than... calculus.

 

l do require assistence though with some PFD or Partial Fractional Decomposition, it's only a part of my proof of divergence (That part doesn't matter for the help).

 

l'm given...

 

4/x(x+2)

 

This conncept just rose from the depths of calculus and l need some help figuring the PFD of that expression. 

HighSchoolCalculus  Feb 14, 2017

Best Answer 

 #4
avatar+75332 
+5

No prob.....!!!!

 

 

cool cool cool

CPhill  Feb 14, 2017
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3+0 Answers

 #1
avatar+75332 
+10

4  / [x (x + 2) ]  =  A / x   +  B / [x + 2]

 

4 / [x (x + 2)] =  [ A(x + 2) + Bx]  / [ x (x + 2))]

 

Since  the denominators are the same, we can solve for the numerators

 

4 = A(x + 2) + Bx

 

4 = Ax + 2A  + Bx

 

0x + 4   = (A + B)x  + 2A

 

Equating coefficients, we have

 

(A + B) = 0

2A  =  4  →   A  = 2

 

So  ( A + B) = 0

 

2 + B  = 0 → B =  - 2

 

So....

 

4  / [x (x + 2) ]  =  2 / x   -  2 / [x + 2]

 

 

cool cool cool

CPhill  Feb 14, 2017
 #2
avatar+1477 
+4

Seems l did the PFD right then. Thanks CP.

HighSchoolCalculus  Feb 14, 2017
 #4
avatar+75332 
+5
Best Answer

No prob.....!!!!

 

 

cool cool cool

CPhill  Feb 14, 2017

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