These are the same partial fraction resolutions of the original term.

Just check your arithmetic, since the two expressions are identical theyThen, 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.

must give the same result.

Either will do, as you see here you get the same result either way.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.

RonL