Partial Fraction Decomp with a constant

[jinksys]

This is throwing me through so many loops.

I have the equation 1/(x^3 + xa^2).

I can not for the life of me decompose this equation.

I use 1(x^3 + xa^2) = A/x + (Bx + C)/(v^2+a^2)

I can get A=1/a^2, but from there progress stops.

All examples on the internet and books only have one variable.

What do I do?

 

[jinksys]

Nevermind, I figured it out.

My second term needs to be (Bx+Cy)/(x^2 + a^2)

 

[Mark44]

Nevermind, I figured it out.

My second term needs to be Bx+Ca/(x^2 + a^2)

You have some extra stuff in there that you don't need, and you are missing some parentheses. The second term should be
$$\frac{Bx + C}{x^2 + a^2}$$

If you write this without using LaTeX, it should be
(Bx + C)/(x² + a²)