Question

Find the partial fraction decomposition of
F(s)=(3s^2+3s+18)/(s^3+9s)

Answer 1

\[\frac{ 3s^2 + 3s + 18 }{ s(s^2 + 9) } = \frac{ A }{ s } +\frac{ Bx + C }{ s^2 + 9 }\]

should I keep going or is this enough?

Answer 2

X?

Answer 3

sorry. Bs + C

Answer 4

so used to using x :P

Answer 5

You'll want to solve for A, B and C

Answer 6

What is the pattern for these kind of questions?

Answer 7

The coefficient numerators are one polynomial order lower than the denominator.

You must reduce the denominator in a multiple of the simplest polynomials.

If it were s^3 -9s we'd have s(s^2 -9) = s(s-3)(s+3) and we'd be dealing with

A/s + B/(s-3) + C/(s+3)

Answer 8

If we had s^4 + 9s in the denominator, we'd be dealing with:

\[\frac{ A }{ s } + \frac{ Bx^2 + Cx + D }{ s^3 + 9 }\]

Answer 9

Or by pattern, do you mean how to solve or A, B and C?

Answer 10

Thx,I get the way!

Answer 11

cool :)

Answer 12

Haha Bs :P . XD .