1. ## Partial Fraction Decomposition

I need some help understanding an apparent discrepancy. In this problem:

4 / (2x^2 - 5x -3) (2x^2 stands for 2x squared)

I find that if I resolve that rational expression to these partial fractions:

(A / 2x + 1) + (B / x - 3)

I get A = -8/7 and B = 4/7

However, if I resolve the rational expression to these partial fractions:

(A / x -3) + (B / 2x + 1)

I get A = 4/7 and B = -8/7

Then, if I let x = 0 and sum the partial fractions I get -4/3 for the first case, and 20/21 for the second case.

I think the first case is correct because the original rational expression (4 / (2x^2 -5x -3)) does resolve to -4/3 when x is set to 0.

So my question is, how does one determine what order to use when resolving rational expressions into partial fractions composed of linear non-repeating factors? It seems to make a big difference in this example, yet my book does not provide guidance in this area.

2. Originally Posted by spiritualfields
I need some help understanding an apparent discrepancy. In this problem:

4 / (2x^2 - 5x -3) (2x^2 stands for 2x squared)

I find that if I resolve that rational expression to these partial fractions:

(A / 2x + 1) + (B / x - 3)

I get A = -8/7 and B = 4/7

However, if I resolve the rational expression to these partial fractions:

(A / x -3) + (B / 2x + 1)

I get A = 4/7 and B = -8/7
These are the same partial fraction resolutions of the original term.

Then, if I let x = 0 and sum the partial fractions I get -4/3 for the first case, and 20/21 for the second case.

I think the first case is correct because the original rational expression (4 / (2x^2 -5x -3)) does resolve to -4/3 when x is set to 0.
Just check your arithmetic, since the two expressions are identical they
must give the same result.

So my question is, how does one determine what order to use when resolving rational expressions into partial fractions composed of linear non-repeating factors? It seems to make a big difference in this example, yet my book does not provide guidance in this area.
Either will do, as you see here you get the same result either way.

RonL

3. Yes, I realize now that I had made an arithmetic error. Thanks.