# Thread: Partial Fractions with Repeated Roots

1. ## Partial Fractions with Repeated Roots

I would appreciate it if somebody could explain why the following applies to partial fractions with repeated roots:

(x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1)^2.

It would make more sense to me if it was as below:

(x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1).

I know this is incorrect however I am unable to find an explanation for why it is done as it is.

2. A/(x+3)+B/(x-1)+C/(x-1).
the least common denominator would be 1/(x+3)(x-1) not 1/(x+3)(x-1)^2 which is what you need

Think about it the least common denominator of 1/2 + 1/2^2 +1/3

is 1/(2^2 *3)

going the other way if you wanted to break 1/(2^2 *3) down into a the most general sum of fractions you would have A/2 + B/2^2 +C/3

same is true of 1/(x-1)^2(x+3)

3. Originally Posted by p75213
I would appreciate it if somebody could explain why the following applies to partial fractions with repeated roots:

(x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1)^2.

It would make more sense to me if it was as below:

(x^2-2x+17)/(x+3)(x-1)^2 = A/(x+3)+B/(x-1)+C/(x-1).

I know this is incorrect however I am unable to find an explanation for why it is done as it is.
Why would that make sense? B/(x-1)+ C/(x-1)= (B+C)/(x-1) so the second fraction adds nothing. And, as Calculus26 told you, after adding the fraction on the right would have denominator (x+3)(x-1), not (x+3)(x-1)^2.

4. Thanks for the explanation Calculus26. The light came on but it took a while. Beats me why it is so difficult to find an explanation on the net.

5. To Hallsofivy,
I was looking for help NOT somebody that starts a post with a critical comment like "Why would that make sense". That being the case I would appreciate it if you didn't reply to any of my posts in the future.