# Integration using partial fractions

#### jpanknin

##### New member
Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?

#### Dr.Peterson

##### Elite Member
Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?
Why would you think order would matter at all? It doesn't. And which constant you call A has no effect on any of the work that follows.

In other words, they are entirely interchangeable. You can do as you wish.

#### Jomo

##### Elite Member
Personally I would use r and s for the constants. Do you think that the solution would change.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?

View attachment 29193
Have you tried switching A & B? What answer do you get?

You should find that the final answer does not depend on that action.