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# Comeback!

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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

#4
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No prob.....!!!!

CPhill  Feb 14, 2017
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#1
+79894
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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]

CPhill  Feb 14, 2017
#2
+1483
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Seems l did the PFD right then. Thanks CP.

HighSchoolCalculus  Feb 14, 2017
#4
+79894
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