partial fraction

**mathaddict** · December 30th 2008, 10:51 PM

Express each of the following in partial fraction .

(a) $\frac{x^2-1}{x^2(2x+1)}$

Is $x^2$ (denominator) , considered as a repeated linear factor ?

(b) $\frac{x^3+3}{(x+1)(x-1)}$

i have tried long division for this question but it doesn't work .

**Isomorphism** · December 30th 2008, 10:59 PM

Originally Posted by mathaddict

Express each of the following in partial fraction .

(a) $\frac{x^2-1}{x^2(2x+1)}$

Is $x^2$ (denominator) , considered as a repeated linear factor ?

Yes.

So $\frac{x^2-1}{x^2(2x+1)} = \frac{Ax+B}{x^2} + \frac{C}{2x+1}$

Get A,B and C by cross multiplying and comparing coefficients.

Originally Posted by mathaddict

(b) $\frac{x^3+3}{(x+1)(x-1)}$

i have tried long division for this question but it doesn't work .

It should. Divide $x^3 + 3$ by $x^2 - 1$ . You will see that:
$\frac{x^3+3}{x^2 - 1} = x + \frac{ x+3 }{x^2 - 1}$

Now do a partial fraction decomposition for $\frac{x+3}{x^2 - 1}$

**mathaddict** · December 30th 2008, 11:21 PM

Originally Posted by Isomorphism

Yes.

So $\frac{x^2-1}{x^2(2x+1)} = \frac{Ax+B}{x^2} + \frac{C}{2x+1}$

Get A,B and C by cross multiplying and comparing coefficients.

Can i do it this way ..
$\frac{x^2-1}{x^2(2x+1)}$
= $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{2x+1}$

**mr fantastic** · December 30th 2008, 11:22 PM

Originally Posted by mathaddict

Can i do it this way ..
$\frac{x^2-1}{x^2(2x+1)}$
= $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{2x+1}$

Yes.

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