# Partial Fraction Decomposition

PBJinx
The equation i currently have is

(-7s+52)/(s^2-8s+16)

I need to convert it into a partial fraction decomposition to do a inverse Laplace Transform, but i seem to be stuck with the algebra of the what I am supposed to do.

The equation I am supposed to use to set them is

A/(s+a) + B/(s+a)^2

What i have done so far is

S^2-8s+16=A/(s-4)+B/(s-4)^2

which then brings me to

A(s-4)^2+B(s-4)=7s+52

solving for A or B being 0 will not work. must I use quadratics to solve?

i am very lost and have been at this one all day

## Answers and Replies

Homework Helper
What i have done so far is

S^2-8s+16=A/(s-4)+B/(s-4)^2
I assume you mean this:
$$\frac{-7s+52}{s^2-8s+16} = \frac{A}{s-4} + \frac{B}{(s-4)^2}$$

which then brings me to

A(s-4)^2+B(s-4)=7s+52
This is wrong. When you multiply both sides by s2 - 8s + 16 you should get
$$-7s + 52 = A(s - 4) + B$$

PBJinx
Ahh. thank you sir, got it right now