Partial Fraction Decomposition

[jdawg]

Homework Statement

(t⁴+9)/(t⁴+9t²)

Homework Equations

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)

 

[Ray Vickson]

Homework Statement

(t⁴+9)/(t⁴+9t²)

Homework Equations

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)

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

 

[jdawg]

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

 

[vela]

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 $t^4+9 = t^4+9t^2-9t^2+9$.

 

[HallsofIvy]

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