# Partial Fraction Decomposition

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

## 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)

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Ray Vickson
Homework Helper
Dearly Missed

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

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

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

vela
Staff Emeritus
Homework Helper
$$1+\frac{9}{t^4+9t^2} = \frac{(t^4+9t^2)+9}{t^4+9t^2} \ne \frac{t^4+9}{t^4+9t^2}$$ You can avoid doing long division by noting that ##t^4+9 = t^4+9t^2-9t^2+9##.