Question

Find the partial fraction decomposition for the ration expression.

(4x^2 + 9x - 8) / x(x+2)^2

So far, I believe the format is
(A/x) + [(Bx+c)/(x+2)^2]

...and I get confused after that. Help plz! Thank you!

Answer 1

ok, multiply the first term by (x^2+4x+4) which is (x+2)^2
and multiply the second term by x
and you get
a(x^2+4 x + 4) + b x^2 + c x = 4 x^2 + 9 x - 8
or
(b+a)x^2 + (c+4a) x + 4 a = 4 x^2 + 9 x - 8
so
4 a = -8
so
a = -2
then
c-8 = 9
c = 17
then
(b+a) = 4
b -2 = 4
b = 6