Resolve into partial fractions $\frac{x^2 + 3x - 5}{(2x - 7)(x^2 + 3)^3}$
The question has to do with the denominator being one linear and a repeated quadratic factor. Although, I am familiar with the aspect of resolving fractions in their partial forms as regards the denominator being repeated linear factors; but with the repeated quadratic, the problem lies before me as a cumbersome task. I really need help in tackling such a problem like this. Thanks!
"Ansatz":
$\frac{(x^2 + 3x - 5)}{(2x - 7)(x^2 + 3)^3}= \frac{A}{2x-7}+\frac{Bx+C}{x^2+3}+\frac{Dx+E}{(x^2+3)^2}+\frac{Fx+G}{(x^2+3)^3}.$