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).
This conncept just rose from the depths of calculus and l need some help figuring the PFD of that expression.
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
4 / [x (x + 2) ] = 2 / x - 2 / [x + 2]