# Math Help - Partial Fraction Expansion

1. ## Partial Fraction Expansion

Hi, this is my first post, so I apologize if it is not formatted correctly. I'm working through a laplace transform for my controls class and I'm having trouble understanding the solution to the example given in class.

$(s^3 + 3s^2 + 1)/((s^2*(s+1)*(s+2))$

Why/how does this expand to $(A/s) + (B/(s^2)) + (C/(s+1)) + (D/(s+2))$?

Mainly, where does that first term (A/s) come from?

Any help would be greatly appreciated. Thanks!

2. ## Re: Partial Fraction Expansion

In general if a fraction has a repeated factor in the denominator then we split it as:
$\frac{T(x)}{(x-a)(x-b)^2}=\frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{(x-b)^2}$

Where $T(x)$ is the numerator.

3. ## Re: Partial Fraction Expansion

Thank you. I appreciate it. I forgot about the repeated factor business.

4. ## Re: Partial Fraction Expansion

You're welcome!