# Partial Fraction Decomposition

1. Feb 11, 2014

### jdawg

1. The problem statement, all variables and given/known data

(t4+9)/(t4+9t2)

2. Relevant equations

3. The attempt at a solution
I'm not completely sure if I'm using the correct method to solve this. Since the degrees of the numerator and denominator are the same, wouldn't you divide the denominator into the numerator? Here is the answer I got:

1+9/(t4+9t2)

2. Feb 11, 2014

### Ray Vickson

$t^4+9t^2 = t^2(t^2+9)$.

3. Feb 11, 2014

### jdawg

Thanks! I was worried that I had done it incorrectly, I'm pretty rusty with division with polynomials.

4. Feb 11, 2014

### vela

Staff Emeritus
You did do it incorrectly.
$$1+\frac{9}{t^4+9t^2} = \frac{(t^4+9t^2)+9}{t^4+9t^2} \ne \frac{t^4+9}{t^4+9t^2}$$ You can avoid doing long division by noting that $t^4+9 = t^4+9t^2-9t^2+9$.

5. Feb 11, 2014