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

#1**+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]

CPhill
Feb 14, 2017